LMFDB - Embedded newform 230.2.l.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	230.17
Dual form			230.2.l.a.203.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.936950 + 0.349464i) q^{2} +(1.92611 - 1.05174i) q^{3} +(0.755750 - 0.654861i) q^{4} +(2.14017 - 0.647831i) q^{5} +(-1.43713 + 1.65853i) q^{6} +(0.903621 + 1.20710i) q^{7} +(-0.479249 + 0.877679i) q^{8} +(0.981834 - 1.52776i) q^{9} +(-1.77883 + 1.35490i) q^{10} +(-1.39727 + 0.638111i) q^{11} +(0.766917 - 2.05618i) q^{12} +(-2.14621 - 1.60663i) q^{13} +(-1.26848 - 0.815205i) q^{14} +(3.44085 - 3.49869i) q^{15} +(0.142315 - 0.989821i) q^{16} +(0.100061 + 1.39903i) q^{17} +(-0.386031 + 1.77455i) q^{18} +(-2.78544 - 3.21457i) q^{19} +(1.19319 - 1.89111i) q^{20} +(3.01002 + 1.37463i) q^{21} +(1.08617 - 1.08617i) q^{22} +(-0.240201 + 4.78981i) q^{23} +2.19455i q^{24} +(4.16063 - 2.77293i) q^{25} +(2.57235 + 0.755311i) q^{26} +(-0.185355 + 2.59161i) q^{27} +(1.47339 + 0.320516i) q^{28} +(-3.52921 - 3.05808i) q^{29} +(-2.00124 + 4.48055i) q^{30} +(4.99090 - 1.46546i) q^{31} +(0.212565 + 0.977147i) q^{32} +(-2.02017 + 2.69863i) q^{33} +(-0.582665 - 1.27586i) q^{34} +(2.71589 + 1.99799i) q^{35} +(-0.258452 - 1.79757i) q^{36} +(0.241444 - 0.0525229i) q^{37} +(3.73320 + 2.03848i) q^{38} +(-5.82360 - 0.837307i) q^{39} +(-0.457085 + 2.18885i) q^{40} +(-3.09304 + 1.98778i) q^{41} +(-3.30062 - 0.236065i) q^{42} +(0.792220 + 1.45084i) q^{43} +(-0.638111 + 1.39727i) q^{44} +(1.11156 - 3.90573i) q^{45} +(-1.44881 - 4.57176i) q^{46} +(0.417418 + 0.417418i) q^{47} +(-0.766917 - 2.05618i) q^{48} +(1.33158 - 4.53494i) q^{49} +(-2.92926 + 4.05209i) q^{50} +(1.66414 + 2.58946i) q^{51} +(-2.67412 + 0.191257i) q^{52} +(-9.06981 + 6.78958i) q^{53} +(-0.732005 - 2.49298i) q^{54} +(-2.57700 + 2.27086i) q^{55} +(-1.49250 + 0.214589i) q^{56} +(-8.74595 - 3.26207i) q^{57} +(4.37539 + 1.63193i) q^{58} +(-14.1593 + 2.03580i) q^{59} +(0.309270 - 4.89741i) q^{60} +(-2.71282 - 9.23902i) q^{61} +(-4.16410 + 3.11721i) q^{62} +(2.73136 - 0.195351i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(-5.63408 - 2.04808i) q^{65} +(0.949723 - 3.23446i) q^{66} +(3.79423 + 10.1727i) q^{67} +(0.991794 + 0.991794i) q^{68} +(4.57497 + 9.47834i) q^{69} +(-3.24288 - 0.922911i) q^{70} +(4.07344 - 8.91960i) q^{71} +(0.870343 + 1.59391i) q^{72} +(-7.82356 - 0.559552i) q^{73} +(-0.207866 + 0.133587i) q^{74} +(5.09744 - 9.71687i) q^{75} +(-4.21019 - 0.605334i) q^{76} +(-2.03286 - 1.11003i) q^{77} +(5.74902 - 1.25062i) q^{78} +(0.466190 + 3.24242i) q^{79} +(-0.336660 - 2.21058i) q^{80} +(4.63192 + 10.1425i) q^{81} +(2.20337 - 2.94335i) q^{82} +(3.47072 + 15.9546i) q^{83} +(3.17501 - 0.932268i) q^{84} +(1.12049 + 2.92935i) q^{85} +(-1.24929 - 1.08251i) q^{86} +(-10.0140 - 2.17840i) q^{87} +(0.109583 - 1.53217i) q^{88} +(14.6523 + 4.30230i) q^{89} +(0.323442 + 4.04792i) q^{90} -4.04247i q^{91} +(2.95513 + 3.77720i) q^{92} +(8.07176 - 8.07176i) q^{93} +(-0.536973 - 0.245227i) q^{94} +(-8.04381 - 5.07522i) q^{95} +(1.43713 + 1.65853i) q^{96} +(3.26012 - 14.9865i) q^{97} +(0.337177 + 4.71435i) q^{98} +(-0.397003 + 2.76121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.936950	+	0.349464i	−0.662524	+	0.247108i
$2$	−0.936950	+	0.349464i	−0.662524	+	0.247108i
$3$	1.92611	−	1.05174i	1.11204	−	0.607220i	0.185210	−	0.982699i	$-0.440703\pi$
$3$	1.92611	−	1.05174i	1.11204	−	0.607220i	0.926831	+	0.375479i	$0.122522\pi$
$4$	0.755750	−	0.654861i	0.377875	−	0.327430i
$5$	2.14017	−	0.647831i	0.957112	−	0.289719i
$5$	2.14017	−	0.647831i	0.957112	−	0.289719i
$6$	−1.43713	+	1.65853i	−0.586704	+	0.677093i
$7$	0.903621	+	1.20710i	0.341536	+	0.456239i	0.938119	−	0.346312i	$-0.112566\pi$
$7$	0.903621	+	1.20710i	0.341536	+	0.456239i	−0.596583	+	0.802551i	$0.703475\pi$
$8$	−0.479249	+	0.877679i	−0.169440	+	0.310306i
$9$	0.981834	−	1.52776i	0.327278	−	0.509255i
$10$	−1.77883	+	1.35490i	−0.562517	+	0.428456i
$11$	−1.39727	+	0.638111i	−0.421292	+	0.192398i	−0.614769	−	0.788707i	$-0.710751\pi$
$11$	−1.39727	+	0.638111i	−0.421292	+	0.192398i	0.193477	+	0.981105i	$0.438024\pi$
$12$	0.766917	−	2.05618i	0.221390	−	0.593569i
$13$	−2.14621	−	1.60663i	−0.595252	−	0.445600i	0.258696	−	0.965959i	$-0.416707\pi$
$13$	−2.14621	−	1.60663i	−0.595252	−	0.445600i	−0.853948	+	0.520359i	$0.825798\pi$
$14$	−1.26848	−	0.815205i	−0.339017	−	0.217873i
$15$	3.44085	−	3.49869i	0.888424	−	0.903357i
$16$	0.142315	−	0.989821i	0.0355787	−	0.247455i
$17$	0.100061	+	1.39903i	0.0242683	+	0.339316i	0.995052	+	0.0993582i	$0.0316790\pi$
$17$	0.100061	+	1.39903i	0.0242683	+	0.339316i	−0.970783	+	0.239958i	$0.922866\pi$
$18$	−0.386031	+	1.77455i	−0.0909883	+	0.418266i
$19$	−2.78544	−	3.21457i	−0.639024	−	0.737473i	0.340178	−	0.940361i	$-0.389513\pi$
$19$	−2.78544	−	3.21457i	−0.639024	−	0.737473i	−0.979202	+	0.202888i	$0.934967\pi$
$20$	1.19319	−	1.89111i	0.266806	−	0.422865i
$21$	3.01002	+	1.37463i	0.656840	+	0.299969i
$22$	1.08617	−	1.08617i	0.231573	−	0.231573i
$23$	−0.240201	+	4.78981i	−0.0500855	+	0.998745i
$23$	−0.240201	+	4.78981i	−0.0500855	+	0.998745i
$24$			2.19455i			0.447961i
$25$	4.16063	−	2.77293i	0.832126	−	0.554587i
$26$	2.57235	+	0.755311i	0.504480	+	0.148129i
$27$	−0.185355	+	2.59161i	−0.0356716	+	0.498755i
$28$	1.47339	+	0.320516i	0.278445	+	0.0605719i
$29$	−3.52921	−	3.05808i	−0.655359	−	0.567872i	0.262425	−	0.964952i	$-0.415478\pi$
$29$	−3.52921	−	3.05808i	−0.655359	−	0.567872i	−0.917784	+	0.397081i	$0.870023\pi$
$30$	−2.00124	+	4.48055i	−0.365375	+	0.818033i
$31$	4.99090	−	1.46546i	0.896393	−	0.263205i	0.199090	−	0.979981i	$-0.436201\pi$
$31$	4.99090	−	1.46546i	0.896393	−	0.263205i	0.697303	+	0.716776i	$0.254383\pi$
$32$	0.212565	+	0.977147i	0.0375766	+	0.172737i
$33$	−2.02017	+	2.69863i	−0.351666	+	0.469771i
$34$	−0.582665	−	1.27586i	−0.0999262	−	0.218808i
$35$	2.71589	+	1.99799i	0.459070	+	0.337722i
$36$	−0.258452	−	1.79757i	−0.0430753	−	0.299595i
$37$	0.241444	−	0.0525229i	0.0396931	−	0.00863471i	−0.192675	−	0.981263i	$-0.561716\pi$
$37$	0.241444	−	0.0525229i	0.0396931	−	0.00863471i	0.232368	+	0.972628i	$0.425353\pi$
$38$	3.73320	+	2.03848i	0.605604	+	0.330685i
$39$	−5.82360	−	0.837307i	−0.932522	−	0.134076i
$40$	−0.457085	+	2.18885i	−0.0722714	+	0.346088i
$41$	−3.09304	+	1.98778i	−0.483052	+	0.310439i	−0.759406	−	0.650617i	$-0.774510\pi$
$41$	−3.09304	+	1.98778i	−0.483052	+	0.310439i	0.276354	+	0.961056i	$0.410874\pi$
$42$	−3.30062	−	0.236065i	−0.509297	−	0.0364256i
$43$	0.792220	+	1.45084i	0.120812	+	0.221251i	0.931085	−	0.364801i	$-0.118863\pi$
$43$	0.792220	+	1.45084i	0.120812	+	0.221251i	−0.810273	+	0.586053i	$0.800681\pi$
$44$	−0.638111	+	1.39727i	−0.0961988	+	0.210646i
$45$	1.11156	−	3.90573i	0.165701	−	0.582232i
$46$	−1.44881	−	4.57176i	−0.213616	−	0.674069i
$47$	0.417418	+	0.417418i	0.0608867	+	0.0608867i	0.736895	−	0.676008i	$-0.236291\pi$
$47$	0.417418	+	0.417418i	0.0608867	+	0.0608867i	−0.676008	+	0.736895i	$0.736291\pi$
$48$	−0.766917	−	2.05618i	−0.110695	−	0.296785i
$49$	1.33158	−	4.53494i	0.190225	−	0.647848i
$50$	−2.92926	+	4.05209i	−0.414260	+	0.573052i
$51$	1.66414	+	2.58946i	0.233027	+	0.362597i
$52$	−2.67412	+	0.191257i	−0.370833	+	0.0265225i
$53$	−9.06981	+	6.78958i	−1.24583	+	0.932620i	−0.999333	−	0.0365223i	$-0.988372\pi$
$53$	−9.06981	+	6.78958i	−1.24583	+	0.932620i	−0.246502	+	0.969142i	$0.579281\pi$
$54$	−0.732005	−	2.49298i	−0.0996132	−	0.339251i
$55$	−2.57700	+	2.27086i	−0.347482	+	0.306202i
$56$	−1.49250	+	0.214589i	−0.199444	+	0.0286757i
$57$	−8.74595	−	3.26207i	−1.15843	−	0.432072i
$58$	4.37539	+	1.63193i	0.574516	+	0.214284i
$59$	−14.1593	+	2.03580i	−1.84338	+	0.265038i	−0.973578	−	0.228357i	$-0.926665\pi$
$59$	−14.1593	+	2.03580i	−1.84338	+	0.265038i	−0.869805	+	0.493395i	$0.835756\pi$
$60$	0.309270	−	4.89741i	0.0399265	−	0.632253i
$61$	−2.71282	−	9.23902i	−0.347341	−	1.18294i	−0.929179	−	0.369631i	$-0.879484\pi$
$61$	−2.71282	−	9.23902i	−0.347341	−	1.18294i	0.581838	−	0.813305i	$-0.302334\pi$
$62$	−4.16410	+	3.11721i	−0.528841	+	0.395886i
$63$	2.73136	−	0.195351i	0.344119	−	0.0246119i
$64$	−0.540641	−	0.841254i	−0.0675801	−	0.105157i
$65$	−5.63408	−	2.04808i	−0.698821	−	0.254033i
$66$	0.949723	−	3.23446i	0.116903	−	0.398134i
$67$	3.79423	+	10.1727i	0.463539	+	1.24279i	0.933011	+	0.359848i	$0.117171\pi$
$67$	3.79423	+	10.1727i	0.463539	+	1.24279i	−0.469472	+	0.882947i	$0.655556\pi$
$68$	0.991794	+	0.991794i	0.120273	+	0.120273i
$69$	4.57497	+	9.47834i	0.550761	+	1.14106i
$70$	−3.24288	−	0.922911i	−0.387599	−	0.110309i
$71$	4.07344	−	8.91960i	0.483429	−	1.05856i	−0.498078	−	0.867132i	$-0.665961\pi$
$71$	4.07344	−	8.91960i	0.483429	−	1.05856i	0.981506	−	0.191429i	$-0.0613121\pi$
$72$	0.870343	+	1.59391i	0.102571	+	0.187845i
$73$	−7.82356	−	0.559552i	−0.915678	−	0.0654906i	−0.394459	−	0.918913i	$-0.629068\pi$
$73$	−7.82356	−	0.559552i	−0.915678	−	0.0654906i	−0.521219	+	0.853423i	$0.674523\pi$
$74$	−0.207866	+	0.133587i	−0.0241639	+	0.0155292i
$75$	5.09744	−	9.71687i	0.588602	−	1.12201i
$76$	−4.21019	−	0.605334i	−0.482942	−	0.0694366i
$77$	−2.03286	−	1.11003i	−0.231666	−	0.126499i
$78$	5.74902	−	1.25062i	0.650949	−	0.141605i
$79$	0.466190	+	3.24242i	0.0524505	+	0.364801i	0.999095	+	0.0425230i	$0.0135396\pi$
$79$	0.466190	+	3.24242i	0.0524505	+	0.364801i	−0.946645	+	0.322278i	$0.895551\pi$
$80$	−0.336660	−	2.21058i	−0.0376397	−	0.247150i
$81$	4.63192	+	10.1425i	0.514658	+	1.12694i
$82$	2.20337	−	2.94335i	0.243321	−	0.325039i
$83$	3.47072	+	15.9546i	0.380961	+	1.75125i	0.624184	+	0.781278i	$0.285432\pi$
$83$	3.47072	+	15.9546i	0.380961	+	1.75125i	−0.243223	+	0.969970i	$0.578205\pi$
$84$	3.17501	−	0.932268i	0.346422	−	0.101719i
$85$	1.12049	+	2.92935i	0.121534	+	0.317732i
$86$	−1.24929	−	1.08251i	−0.134714	−	0.116730i
$87$	−10.0140	−	2.17840i	−1.07361	−	0.233549i
$88$	0.109583	−	1.53217i	0.0116816	−	0.163330i
$89$	14.6523	+	4.30230i	1.55314	+	0.456043i	0.942037	−	0.335508i	$-0.108908\pi$
$89$	14.6523	+	4.30230i	1.55314	+	0.456043i	0.611103	+	0.791551i	$0.290726\pi$
$90$	0.323442	+	4.04792i	0.0340938	+	0.426689i
$91$		−	4.04247i		−	0.423766i
$92$	2.95513	+	3.77720i	0.308093	+	0.393800i
$93$	8.07176	−	8.07176i	0.837003	−	0.837003i
$94$	−0.536973	−	0.245227i	−0.0553845	−	0.0252933i
$95$	−8.04381	−	5.07522i	−0.825278	−	0.520707i
$96$	1.43713	+	1.65853i	0.146676	+	0.169273i
$97$	3.26012	−	14.9865i	0.331015	−	1.52165i	−0.447649	−	0.894209i	$-0.647739\pi$
$97$	3.26012	−	14.9865i	0.331015	−	1.52165i	0.778664	−	0.627441i	$-0.215898\pi$
$98$	0.337177	+	4.71435i	0.0340600	+	0.476221i
$99$	−0.397003	+	2.76121i	−0.0399003	+	0.277513i
$100$	1.32851	−	4.82028i	0.132851	−	0.482028i
$101$	−0.930194	−	0.597800i	−0.0925578	−	0.0594833i	0.493543	−	0.869721i	$-0.335701\pi$
$101$	−0.930194	−	0.597800i	−0.0925578	−	0.0594833i	−0.586101	+	0.810238i	$0.699338\pi$
$102$	−2.46414	−	1.84463i	−0.243987	−	0.182646i
$103$	−0.297569	+	0.797815i	−0.0293204	+	0.0786110i	−0.950785	−	0.309851i	$-0.899721\pi$
$103$	−0.297569	+	0.797815i	−0.0293204	+	0.0786110i	0.921465	+	0.388462i	$0.126994\pi$
$104$	2.43868	−	1.11371i	0.239132	−	0.109208i
$105$	7.33248	+	0.991952i	0.715576	+	0.0968046i
$106$	6.12524	−	9.53107i	0.594936	−	0.925739i
$107$	−4.67977	+	8.57035i	−0.452410	+	0.828527i	−0.999966	−	0.00824183i	$-0.997377\pi$
$107$	−4.67977	+	8.57035i	−0.452410	+	0.828527i	0.547556	+	0.836769i	$0.315558\pi$
$108$	1.55706	+	2.07999i	0.149828	+	0.200147i
$109$	5.27597	−	6.08880i	0.505346	−	0.583201i	−0.444555	−	0.895752i	$-0.646638\pi$
$109$	5.27597	−	6.08880i	0.505346	−	0.583201i	0.949901	+	0.312551i	$0.101183\pi$
$110$	1.62093	−	3.02825i	0.154550	−	0.288732i
$111$	0.409808	−	0.355100i	0.0388972	−	0.0337046i
$112$	1.32341	−	0.722635i	0.125050	−	0.0682826i
$113$	12.7462	−	4.75409i	1.19906	−	0.447227i	0.330976	−	0.943639i	$-0.392622\pi$
$113$	12.7462	−	4.75409i	1.19906	−	0.447227i	0.868087	+	0.496412i	$0.165349\pi$
$114$	9.33450			0.874256
$115$	2.58892	+	10.4066i	0.241418	+	0.970421i
$116$	−4.66982			−0.433582
$117$	−4.56178	+	1.70146i	−0.421737	+	0.157300i
$118$	12.5551	−	6.85561i	1.15579	−	0.631110i
$119$	−1.59835	+	1.38498i	−0.146521	+	0.126961i
$120$	1.42170	+	4.69671i	0.129783	+	0.428749i
$121$	−5.65830	+	6.53002i	−0.514390	+	0.593638i
$122$	5.77048	+	7.70847i	0.522435	+	0.697892i
$123$	−3.86692	+	7.08174i	−0.348669	+	0.638539i
$124$	2.81220	−	4.37587i	0.252543	−	0.392965i
$125$	7.10805	−	8.62993i	0.635763	−	0.771884i
$126$	−2.49088	+	1.13755i	−0.221905	+	0.101341i
$127$	4.73936	−	12.7067i	0.420551	−	1.12754i	−0.538082	−	0.842893i	$-0.680851\pi$
$127$	4.73936	−	12.7067i	0.420551	−	1.12754i	0.958632	−	0.284647i	$-0.0918764\pi$
$128$	0.800541	+	0.599278i	0.0707585	+	0.0529692i
$129$	3.05181	+	1.96128i	0.268697	+	0.172681i
$130$	5.99458	−	0.0499597i	0.525759	−	0.00438175i
$131$	−2.35552	+	16.3830i	−0.205803	+	1.43139i	0.580858	+	0.814005i	$0.302717\pi$
$131$	−2.35552	+	16.3830i	−0.205803	+	1.43139i	−0.786661	+	0.617385i	$0.788192\pi$
$132$	0.240485	+	3.36242i	0.0209315	+	0.292661i
$133$	1.36331	−	6.26705i	0.118214	−	0.543422i
$134$	−7.11000	−	8.20538i	−0.614210	−	0.708837i
$135$	1.28223	+	5.66655i	0.110357	+	0.487699i
$136$	−1.27586	−	0.582665i	−0.109404	−	0.0499631i
$137$	13.6458	−	13.6458i	1.16584	−	1.16584i	0.182667	−	0.983175i	$-0.441527\pi$
$137$	13.6458	−	13.6458i	1.16584	−	1.16584i	0.983175	−	0.182667i	$-0.0584732\pi$
$138$	−7.59885	−	7.28194i	−0.646857	−	0.619880i
$139$			16.2156i			1.37539i	0.726000	+	0.687694i	$0.241377\pi$
$139$			16.2156i			1.37539i	−0.726000	+	0.687694i	$0.758623\pi$
$140$	3.36094	−	0.268550i	0.284051	−	0.0226966i
$141$	1.24301	+	0.364980i	0.104680	+	0.0307369i
$142$	−0.699532	+	9.78074i	−0.0587034	+	0.820781i
$143$	4.02404	+	0.875377i	0.336507	+	0.0732027i
$144$	−1.37248	−	1.18926i	−0.114374	−	0.0991053i
$145$	−9.53423	−	4.25847i	−0.791775	−	0.353647i
$146$	7.52582	−	2.20978i	0.622842	−	0.182883i
$147$	−2.20479	−	10.1353i	−0.181848	−	0.835943i
$148$	0.148076	−	0.197806i	0.0121718	−	0.0162596i
$149$	−4.26348	−	9.33572i	−0.349278	−	0.764812i	−0.999985	−	0.00548319i	$-0.998255\pi$
$149$	−4.26348	−	9.33572i	−0.349278	−	0.764812i	0.650707	−	0.759329i	$-0.274473\pi$
$150$	−1.38035	+	10.8856i	−0.112705	+	0.888805i
$151$	−1.59788	−	11.1135i	−0.130034	−	0.904404i	−0.945505	−	0.325607i	$-0.894431\pi$
$151$	−1.59788	−	11.1135i	−0.130034	−	0.904404i	0.815472	−	0.578797i	$-0.196478\pi$
$152$	4.15628	−	0.904144i	0.337119	−	0.0733357i
$153$	2.23564	+	1.22075i	0.180741	+	0.0986918i
$154$	2.29260	+	0.329627i	0.184743	+	0.0265621i
$155$	9.73200	−	6.36960i	0.781693	−	0.511618i
$156$	−4.94950	+	3.18085i	−0.396277	+	0.254672i
$157$	2.06168	+	0.147454i	0.164540	+	0.0117681i	0.153366	−	0.988169i	$-0.450989\pi$
$157$	2.06168	+	0.147454i	0.164540	+	0.0117681i	0.0111740	+	0.999938i	$0.496443\pi$
$158$	−1.56991	−	2.87507i	−0.124895	−	0.228728i
$159$	−10.3286	+	22.6165i	−0.819113	+	1.79361i
$160$	1.08795	+	1.95355i	0.0860101	+	0.154442i
$161$	−5.99881	+	4.03823i	−0.472773	+	0.318257i
$162$	−7.88432	−	7.88432i	−0.619450	−	0.619450i
$163$	0.0105853	+	0.0283803i	0.000829104	+	0.00222291i	0.937364	−	0.348352i	$-0.113259\pi$
$163$	0.0105853	+	0.0283803i	0.000829104	+	0.00222291i	−0.936535	+	0.350575i	$0.885986\pi$
$164$	−1.03585	+	3.52777i	−0.0808861	+	0.275473i
$165$	−2.57524	+	7.08425i	−0.200482	+	0.551508i
$166$	−8.82746	−	13.7358i	−0.685144	−	1.06610i
$167$	2.01561	−	0.144159i	0.155972	−	0.0111554i	0.00686544	−	0.999976i	$-0.497815\pi$
$167$	2.01561	−	0.144159i	0.155972	−	0.0111554i	0.149107	+	0.988821i	$0.452360\pi$
$168$	−2.64903	+	1.98304i	−0.204377	+	0.152995i
$169$	−1.63757	−	5.57707i	−0.125967	−	0.429005i
$170$	−2.07354	−	2.35308i	−0.159033	−	0.180473i
$171$	−7.64595	+	1.09932i	−0.584700	+	0.0840672i
$172$	1.54882	+	0.577680i	0.118096	+	0.0440477i
$173$	−21.7727	−	8.12081i	−1.65535	−	0.617414i	−0.663891	−	0.747829i	$-0.731096\pi$
$173$	−21.7727	−	8.12081i	−1.65535	−	0.617414i	−0.991459	+	0.130415i	$0.958369\pi$
$174$	10.1438	−	1.45847i	0.769003	−	0.110566i
$175$	7.10683	+	2.51660i	0.537226	+	0.190237i
$176$	0.432764	+	1.47386i	0.0326208	+	0.111096i
$177$	−25.1313	+	18.8130i	−1.88898	+	1.41407i
$178$	−15.2320	+	1.08941i	−1.14168	+	0.0816549i
$179$	−12.2936	−	19.1293i	−0.918871	−	1.42979i	−0.902868	−	0.429919i	$-0.858542\pi$
$179$	−12.2936	−	19.1293i	−0.918871	−	1.42979i	−0.0160028	−	0.999872i	$-0.505094\pi$
$180$	−1.71765	−	3.67967i	−0.128026	−	0.274266i
$181$	−2.48139	+	8.45084i	−0.184440	+	0.628146i	0.814414	+	0.580285i	$0.197059\pi$
$181$	−2.48139	+	8.45084i	−0.184440	+	0.628146i	−0.998854	+	0.0478613i	$0.984759\pi$
$182$	1.41270	+	3.78759i	0.104716	+	0.280755i
$183$	−14.9422	−	14.9422i	−1.10456	−	1.10456i
$184$	−4.08880	−	2.50633i	−0.301430	−	0.184769i
$185$	0.482704	−	0.268823i	0.0354891	−	0.0197642i
$186$	−4.74204	+	10.3836i	−0.347703	+	0.761364i
$187$	−1.03255	−	1.89098i	−0.0755076	−	0.138282i
$188$	0.588815	+	0.0421129i	0.0429437	+	0.00307140i
$189$	−3.29581	+	2.11809i	−0.239735	+	0.154068i
$190$	9.31026	+	1.94420i	0.675437	+	0.141047i
$191$	12.4824	+	1.79470i	0.903194	+	0.129860i	0.578237	−	0.815869i	$-0.303741\pi$
$191$	12.4824	+	1.79470i	0.903194	+	0.129860i	0.324957	+	0.945729i	$0.394650\pi$
$192$	−1.92611	−	1.05174i	−0.139005	−	0.0759025i
$193$	−2.75997	+	0.600396i	−0.198667	+	0.0432174i	−0.310798	−	0.950476i	$-0.600596\pi$
$193$	−2.75997	+	0.600396i	−0.198667	+	0.0432174i	0.112130	+	0.993693i	$0.464233\pi$
$194$	2.18269	+	15.1809i	0.156708	+	1.08993i
$195$	−13.0059	+	1.98073i	−0.931372	+	0.141843i
$196$	−1.96341	−	4.29928i	−0.140244	−	0.307091i
$197$	12.7225	−	16.9952i	0.906437	−	1.21086i	−0.0705388	−	0.997509i	$-0.522472\pi$
$197$	12.7225	−	16.9952i	0.906437	−	1.21086i	0.976976	−	0.213349i	$-0.0684372\pi$
$198$	−0.592974	−	2.72586i	−0.0421408	−	0.193718i
$199$	−5.32380	+	1.56321i	−0.377394	+	0.110813i	−0.464928	−	0.885349i	$-0.653920\pi$
$199$	−5.32380	+	1.56321i	−0.377394	+	0.110813i	0.0875334	+	0.996162i	$0.472102\pi$
$200$	0.439770	+	4.98062i	0.0310964	+	0.352183i
$201$	18.0071	+	15.6033i	1.27012	+	1.10057i
$202$	1.08045	+	0.235039i	0.0760205	+	0.0165373i
$203$	0.502327	−	7.02345i	0.0352564	−	0.492949i
$204$	2.95341	+	0.867200i	0.206780	+	0.0607161i
$205$	−5.33188	+	6.25794i	−0.372395	+	0.437074i
$206$		−	0.851502i		−	0.0593270i
$207$	7.08186	+	5.06977i	0.492224	+	0.352374i
$208$	−1.89572	+	1.89572i	−0.131444	+	0.131444i
$209$	5.94326	+	2.71420i	0.411104	+	0.187745i
$210$	−7.21681	+	1.63303i	−0.498007	+	0.112690i
$211$	11.3736	+	13.1259i	0.782992	+	0.903621i	0.997322	−	0.0731402i	$-0.0233021\pi$
$211$	11.3736	+	13.1259i	0.782992	+	0.903621i	−0.214329	+	0.976761i	$0.568757\pi$
$212$	−2.40828	+	11.0707i	−0.165401	+	0.760338i
$213$	−1.53516	−	21.4643i	−0.105187	−	1.47071i
$214$	1.38967	−	9.66540i	0.0949962	−	0.660713i
$215$	2.63538	+	2.59182i	0.179732	+	0.176761i
$216$	−2.18577	−	1.40471i	−0.148723	−	0.0955782i
$217$	6.27884	+	4.70028i	0.426235	+	0.319076i
$218$	−2.81550	+	7.54866i	−0.190690	+	0.511260i
$219$	−15.6575	+	7.15056i	−1.05804	+	0.483190i
$220$	−0.460470	+	3.40378i	−0.0310449	+	0.229482i
$221$	2.03298	−	3.16338i	0.136753	−	0.212792i
$222$	−0.259874	+	0.475924i	−0.0174416	+	0.0319419i
$223$	−6.41582	−	8.57054i	−0.429635	−	0.573926i	0.532523	−	0.846415i	$-0.321244\pi$
$223$	−6.41582	−	8.57054i	−0.429635	−	0.573926i	−0.962159	+	0.272490i	$0.912153\pi$
$224$	−0.987431	+	1.13956i	−0.0659755	+	0.0761398i
$225$	−0.151342	−	9.07902i	−0.0100895	−	0.605268i
$226$	−10.2812	+	8.90869i	−0.683894	+	0.592597i
$227$	10.8998	−	5.95173i	0.723443	−	0.395030i	−0.0749330	−	0.997189i	$-0.523874\pi$
$227$	10.8998	−	5.95173i	0.723443	−	0.395030i	0.798377	+	0.602159i	$0.205692\pi$
$228$	−8.74595	+	3.26207i	−0.579215	+	0.216036i
$229$	15.9267			1.05247			0.526233	−	0.850340i	$-0.323604\pi$
$229$	15.9267			1.05247			0.526233	+	0.850340i	$0.323604\pi$
$230$	−6.06242	−	8.84573i	−0.399744	−	0.583270i
$231$	−5.08297			−0.334435
$232$	4.37539	−	1.63193i	0.287258	−	0.107142i
$233$	4.60608	−	2.51511i	0.301755	−	0.164770i	−0.321237	−	0.946999i	$-0.604099\pi$
$233$	4.60608	−	2.51511i	0.301755	−	0.164770i	0.622992	+	0.782228i	$0.285917\pi$
$234$	3.67956	−	3.18836i	0.240540	−	0.208429i
$235$	1.16376	+	0.622928i	0.0759155	+	0.0406354i
$236$	−9.36771	+	10.8109i	−0.609786	+	0.703731i
$237$	4.30811	+	5.75496i	0.279842	+	0.373825i
$238$	1.01357	−	1.85622i	0.0657003	−	0.120321i
$239$	12.8396	−	19.9789i	0.830527	−	1.29233i	−0.123421	−	0.992354i	$-0.539387\pi$
$239$	12.8396	−	19.9789i	0.830527	−	1.29233i	0.953948	−	0.299971i	$-0.0969771\pi$
$240$	−2.97339	−	3.90374i	−0.191932	−	0.251986i
$241$	10.5483	−	4.81724i	0.679474	−	0.310306i	−0.0456163	−	0.998959i	$-0.514525\pi$
$241$	10.5483	−	4.81724i	0.679474	−	0.310306i	0.725091	+	0.688654i	$0.241798\pi$
$242$	3.01953	−	8.09567i	0.194103	−	0.520410i
$243$	13.3489	+	9.99284i	0.856331	+	0.641041i
$244$	−8.10049	−	5.20587i	−0.518581	−	0.333271i
$245$	−0.0880766	−	10.5682i	−0.00562701	−	0.675175i
$246$	1.14830	−	7.98659i	0.0732128	−	0.509206i
$247$	0.813508	+	11.3743i	0.0517623	+	0.723731i
$248$	−1.10568	+	5.08273i	−0.0702108	+	0.322754i
$249$	23.4651	+	27.0801i	1.48704	+	1.71613i
$250$	−3.64403	+	10.5698i	−0.230469	+	0.668494i
$251$	4.99303	+	2.28024i	0.315157	+	0.143927i	0.566713	−	0.823915i	$-0.308215\pi$
$251$	4.99303	+	2.28024i	0.315157	+	0.143927i	−0.251556	+	0.967843i	$0.580942\pi$
$252$	1.93630	−	1.93630i	0.121975	−	0.121975i
$253$	−2.72081	−	6.84593i	−0.171056	−	0.430400i
$254$			13.5618i			0.850943i
$255$	5.23908	+	4.46379i	0.328084	+	0.279533i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−0.0487273	+	0.681296i	−0.00303952	+	0.0424981i	−0.998746	−	0.0500739i	$-0.984054\pi$
$257$	−0.0487273	+	0.681296i	−0.00303952	+	0.0424981i	0.995706	+	0.0925720i	$0.0295088\pi$
$258$	−3.54479	−	0.771121i	−0.220689	−	0.0480079i
$259$	0.281574	+	0.243985i	0.0174961	+	0.0151605i
$260$	−5.59916	+	2.14170i	−0.347245	+	0.132823i
$261$	−8.13713	+	2.38928i	−0.503676	+	0.147893i
$262$	−3.51827	−	16.1732i	−0.217359	−	0.999185i
$263$	4.23997	−	5.66394i	0.261448	−	0.349253i	−0.650539	−	0.759473i	$-0.725457\pi$
$263$	4.23997	−	5.66394i	0.261448	−	0.349253i	0.911987	+	0.410219i	$0.134548\pi$
$264$	−1.40037	−	3.06638i	−0.0861867	−	0.188722i
$265$	−15.0124	+	20.4065i	−0.922205	+	1.25356i
$266$	0.912753	+	6.34834i	0.0559645	+	0.389242i
$267$	32.7469	−	7.12364i	2.00408	−	0.435960i
$268$	9.52920	+	5.20333i	0.582088	+	0.317844i
$269$	−22.7194	−	3.26656i	−1.38523	−	0.199165i	−0.590943	−	0.806713i	$-0.701244\pi$
$269$	−22.7194	−	3.26656i	−1.38523	−	0.199165i	−0.794283	+	0.607548i	$0.792153\pi$
$270$	−3.18164	−	4.86118i	−0.193629	−	0.295842i
$271$	−4.43331	+	2.84912i	−0.269305	+	0.173072i	−0.668323	−	0.743871i	$-0.732987\pi$
$271$	−4.43331	+	2.84912i	−0.269305	+	0.173072i	0.399018	+	0.916943i	$0.369351\pi$
$272$	1.39903	+	0.100061i	0.0848289	+	0.00606709i
$273$	−4.25161	−	7.78624i	−0.257319	−	0.471245i
$274$	−8.01673	+	17.5542i	−0.484308	+	1.06049i
$275$	−4.04407	+	6.52948i	−0.243867	+	0.393742i
$276$	9.66452	+	4.16729i	0.581736	+	0.250841i
$277$	7.49106	+	7.49106i	0.450094	+	0.450094i	0.895386	−	0.445292i	$-0.146900\pi$
$277$	7.49106	+	7.49106i	0.450094	+	0.450094i	−0.445292	+	0.895386i	$0.646900\pi$
$278$	−5.66677	−	15.1932i	−0.339870	−	0.911227i
$279$	2.66136	−	9.06376i	0.159332	−	0.542633i
$280$	−3.05519	+	1.42615i	−0.182582	+	0.0852286i
$281$	1.49674	+	2.32898i	0.0892883	+	0.138935i	0.883025	−	0.469327i	$-0.155503\pi$
$281$	1.49674	+	2.32898i	0.0892883	+	0.138935i	−0.793736	+	0.608262i	$0.791867\pi$
$282$	−1.29218	+	0.0924189i	−0.0769485	+	0.00550346i
$283$	15.3849	−	11.5170i	0.914535	−	0.684612i	−0.0346271	−	0.999400i	$-0.511024\pi$
$283$	15.3849	−	11.5170i	0.914535	−	0.684612i	0.949162	+	0.314788i	$0.101933\pi$
$284$	−2.76259	−	9.40852i	−0.163930	−	0.558293i
$285$	−20.8311	−	1.31547i	−1.23393	−	0.0779220i
$286$	−4.07624	+	0.586074i	−0.241033	+	0.0346553i
$287$	−5.19437	−	1.93740i	−0.306614	−	0.114361i
$288$	1.70155	+	0.634647i	0.100265	+	0.0373969i
$289$	14.8797	−	2.13937i	0.875275	−	0.125846i
$290$	10.4213	+	0.658100i	0.611958	+	0.0386449i
$291$	−9.48252	−	32.2945i	−0.555875	−	1.89314i
$292$	−6.27908	+	4.70046i	−0.367455	+	0.275074i
$293$	−17.3386	+	1.24008i	−1.01293	+	0.0724463i	−0.567924	−	0.823081i	$-0.692253\pi$
$293$	−17.3386	+	1.24008i	−1.01293	+	0.0724463i	−0.445007	+	0.895527i	$0.646799\pi$
$294$	5.60769	+	8.72574i	0.327047	+	0.508895i
$295$	−28.9844	+	13.5298i	−1.68754	+	0.787735i
$296$	−0.0696135	+	0.237082i	−0.00404620	+	0.0137801i
$297$	−1.39474	−	3.73945i	−0.0809311	−	0.216985i
$298$	7.25717	+	7.25717i	0.420396	+	0.420396i
$299$	8.21099	−	9.89403i	0.474854	−	0.572186i
$300$	−2.51081	−	10.6816i	−0.144962	−	0.616704i
$301$	−1.03544	+	2.26730i	−0.0596817	+	0.130685i
$302$	5.38090	+	9.85439i	0.309636	+	0.567056i
$303$	−2.42039	−	0.173109i	−0.139048	−	0.00994487i
$304$	−3.57826	+	2.29961i	−0.205227	+	0.131892i
$305$	−11.7912	−	18.0156i	−0.675163	−	1.03157i
$306$	−2.52129	−	0.362507i	−0.144132	−	0.0207231i
$307$	−19.3648	−	10.5740i	−1.10521	−	0.603488i	−0.180272	−	0.983617i	$-0.557698\pi$
$307$	−19.3648	−	10.5740i	−1.10521	−	0.603488i	−0.924933	+	0.380129i	$0.875880\pi$
$308$	−2.26325	+	0.492339i	−0.128960	+	0.0280536i
$309$	0.265939	+	1.84964i	0.0151287	+	0.105223i
$310$	−6.89245	+	9.36898i	−0.391465	+	0.532122i
$311$	−2.46940	−	5.40724i	−0.140027	−	0.306616i	0.826606	−	0.562781i	$-0.190268\pi$
$311$	−2.46940	−	5.40724i	−0.140027	−	0.306616i	−0.966633	+	0.256164i	$0.917541\pi$
$312$	3.52584	−	4.70997i	0.199611	−	0.266649i
$313$	3.48497	+	16.0201i	0.196982	+	0.905512i	0.964417	+	0.264385i	$0.0851690\pi$
$313$	3.48497	+	16.0201i	0.196982	+	0.905512i	−0.767435	+	0.641127i	$0.778467\pi$
$314$	−1.98322	+	0.582327i	−0.111920	+	0.0328626i
$315$	5.71902	−	2.18755i	0.322230	−	0.123254i
$316$	2.47566	+	2.14517i	0.139267	+	0.120675i
$317$	6.07871	+	1.32234i	0.341414	+	0.0742701i	0.380004	−	0.924985i	$-0.375923\pi$
$317$	6.07871	+	1.32234i	0.341414	+	0.0742701i	−0.0385893	+	0.999255i	$0.512286\pi$
$318$	1.77373	−	24.8000i	0.0994661	−	1.39072i
$319$	6.88266	+	2.02093i	0.385355	+	0.113150i
$320$	−1.70205	−	1.45018i	−0.0951476	−	0.0810675i
$321$			21.4293i			1.19607i
$322$	4.20937	−	5.87999i	0.234579	−	0.327679i
$323$	4.21858	−	4.21858i	0.234728	−	0.234728i
$324$	10.1425	+	4.63192i	0.563472	+	0.257329i
$325$	−13.3847	−	0.733301i	−0.742448	−	0.0406762i
$326$	−0.0198358	−	0.0228917i	−0.00109860	−	0.00126785i
$327$	3.75830	−	17.2766i	0.207835	−	0.955400i
$328$	−0.262293	−	3.66734i	−0.0144827	−	0.202495i
$329$	−0.126676	+	0.881052i	−0.00698388	+	0.0485740i
$330$	−0.0628189	−	7.53754i	−0.00345807	−	0.414928i
$331$	0.434379	+	0.279158i	0.0238756	+	0.0153439i	0.552524	−	0.833497i	$-0.313665\pi$
$331$	0.434379	+	0.279158i	0.0238756	+	0.0153439i	−0.528649	+	0.848841i	$0.677301\pi$
$332$	13.0711	+	9.78487i	0.717367	+	0.537014i
$333$	0.156815	−	0.420438i	0.00859342	−	0.0230399i
$334$	−1.83815	+	0.839453i	−0.100579	+	0.0459328i
$335$	14.7105	+	19.3133i	0.803720	+	1.05520i
$336$	1.78901	−	2.78375i	0.0975985	−	0.151866i
$337$	−12.4437	+	22.7889i	−0.677850	+	1.24139i	0.281606	+	0.959530i	$0.409133\pi$
$337$	−12.4437	+	22.7889i	−0.677850	+	1.24139i	−0.959456	+	0.281860i	$0.909049\pi$
$338$	3.48331	+	4.65316i	0.189467	+	0.253098i
$339$	19.5506	−	22.5626i	1.06184	−	1.22543i
$340$	2.76512	+	1.48009i	0.149960	+	0.0802691i
$341$	−6.03851	+	5.23239i	−0.327003	+	0.283350i
$342$	6.77970	−	3.70199i	0.366604	−	0.200181i
$343$	16.5668	−	6.17910i	0.894523	−	0.333640i
$344$	−1.65304			−0.0891262
$345$	15.9316	+	17.3214i	0.857726	+	0.932554i
$346$	23.2379			1.24928
$347$	14.3383	−	5.34792i	0.769722	−	0.287091i	0.0662391	−	0.997804i	$-0.478900\pi$
$347$	14.3383	−	5.34792i	0.769722	−	0.287091i	0.703483	+	0.710712i	$0.251627\pi$
$348$	−8.99460	+	4.91142i	−0.482161	+	0.263280i
$349$	15.4328	−	13.3726i	0.826096	−	0.715816i	−0.135353	−	0.990797i	$-0.543217\pi$
$349$	15.4328	−	13.3726i	0.826096	−	0.715816i	0.961450	+	0.274981i	$0.0886715\pi$
$350$	−7.53820	+	0.125658i	−0.402934	+	0.00671668i
$351$	4.56157	−	5.26433i	0.243479	−	0.280989i
$352$	−0.920539	−	1.22970i	−0.0490649	−	0.0655430i
$353$	−10.8649	+	19.8975i	−0.578278	+	1.05904i	0.410811	+	0.911721i	$0.365246\pi$
$353$	−10.8649	+	19.8975i	−0.578278	+	1.05904i	−0.989089	+	0.147317i	$0.952936\pi$
$354$	16.9722	−	26.4093i	0.902065	−	1.40364i
$355$	2.93945	−	21.7283i	0.156010	−	1.15322i
$356$	13.8909	−	6.34375i	0.736215	−	0.336218i
$357$	−1.62197	+	4.34867i	−0.0858438	+	0.230156i
$358$	18.2035	+	13.6270i	0.962087	+	0.720209i
$359$	−1.60206	−	1.02958i	−0.0845536	−	0.0543393i	0.497681	−	0.867360i	$-0.334185\pi$
$359$	−1.60206	−	1.02958i	−0.0845536	−	0.0543393i	−0.582234	+	0.813021i	$0.697821\pi$
$360$	2.89527	+	2.84741i	0.152594	+	0.150072i
$361$	0.129200	−	0.898603i	0.00679998	−	0.0472949i
$362$	−0.628328	−	8.78517i	−0.0330242	−	0.461738i
$363$	−4.03065	+	18.5286i	−0.211554	+	0.972499i
$364$	−2.64725	−	3.05509i	−0.138754	−	0.160130i
$365$	−17.1062	+	3.87081i	−0.895380	+	0.202608i
$366$	19.2219	+	8.77834i	1.00474	+	0.458851i
$367$	−19.0241	+	19.0241i	−0.993048	+	0.993048i	−0.999976	−	0.00692833i	$-0.997795\pi$
$367$	−19.0241	+	19.0241i	−0.993048	+	0.993048i	0.00692833	+	0.999976i	$0.497795\pi$
$368$	4.70687	+	0.919418i	0.245363	+	0.0479280i
$369$			6.67710i			0.347596i
$370$	−0.358326	+	0.420561i	−0.0186285	+	0.0218639i
$371$	−16.3913	−	4.81293i	−0.850996	−	0.249875i
$372$	0.814351	−	11.3861i	0.0422221	−	0.590342i
$373$	12.8517	+	2.79571i	0.665435	+	0.144756i	0.532581	−	0.846379i	$-0.321222\pi$
$373$	12.8517	+	2.79571i	0.665435	+	0.144756i	0.132854	+	0.991136i	$0.457586\pi$
$374$	1.62828	+	1.41091i	0.0841962	+	0.0729564i
$375$	4.61448	−	24.0980i	0.238291	−	1.24442i
$376$	−0.566407	+	0.166312i	−0.0292102	+	0.00857689i
$377$	2.66122	+	12.2334i	0.137060	+	0.630054i
$378$	2.34781	−	3.13631i	0.120758	−	0.161314i
$379$	−8.76220	−	19.1865i	−0.450084	−	0.985547i	−0.989637	−	0.143595i	$-0.954134\pi$
$379$	−8.76220	−	19.1865i	−0.450084	−	0.985547i	0.539552	−	0.841952i	$-0.318593\pi$
$380$	−9.40267	+	1.43198i	−0.482347	+	0.0734590i
$381$	−4.23558	−	29.4591i	−0.216996	−	1.50924i
$382$	−12.3225	+	2.68061i	−0.630476	+	0.137152i
$383$	9.29505	+	5.07548i	0.474955	+	0.259345i	0.698850	−	0.715268i	$-0.253695\pi$
$383$	9.29505	+	5.07548i	0.474955	+	0.259345i	−0.223895	+	0.974613i	$0.571877\pi$
$384$	2.17221	+	0.312317i	0.110850	+	0.0159379i
$385$	−5.06977	−	1.05869i	−0.258380	−	0.0539558i
$386$	2.37614	−	1.52705i	0.120942	−	0.0777249i
$387$	2.99437	+	0.214162i	0.152213	+	0.0108865i
$388$	−7.35025	−	13.4610i	−0.373152	−	0.683378i
$389$	−2.31542	+	5.07007i	−0.117397	+	0.257063i	−0.959204	−	0.282716i	$-0.908765\pi$
$389$	−2.31542	+	5.07007i	−0.117397	+	0.257063i	0.841807	+	0.539778i	$0.181492\pi$
$390$	11.4937	−	6.40094i	0.582005	−	0.324124i
$391$	−6.72515	+	0.143223i	−0.340105	+	0.00724310i
$392$	3.34206	+	3.34206i	0.168800	+	0.168800i
$393$	12.6936	+	34.0329i	0.640308	+	1.71673i
$394$	−5.98108	+	20.3697i	−0.301323	+	1.02621i
$395$	3.09827	+	6.63732i	0.155891	+	0.333960i
$396$	1.50818	+	2.34677i	0.0757887	+	0.117930i
$397$	−30.0652	+	2.15031i	−1.50893	+	0.107921i	−0.801129	−	0.598491i	$-0.795767\pi$
$397$	−30.0652	+	2.15031i	−1.50893	+	0.107921i	−0.707801	+	0.706412i	$0.750313\pi$
$398$	4.44185	−	3.32513i	0.222650	−	0.166674i
$399$	−3.96539	−	13.5049i	−0.198518	−	0.676090i
$400$	−2.15259	−	4.51291i	−0.107630	−	0.225645i
$401$	−6.08458	+	0.874831i	−0.303849	+	0.0436870i	−0.292553	−	0.956249i	$-0.594505\pi$
$401$	−6.08458	+	0.874831i	−0.303849	+	0.0436870i	−0.0112962	+	0.999936i	$0.503596\pi$
$402$	−22.3245	−	8.32663i	−1.11345	−	0.415294i
$403$	−13.0660	−	4.87336i	−0.650863	−	0.242759i
$404$	−1.09447	+	0.157361i	−0.0544519	+	0.00782900i
$405$	16.4837	+	18.7059i	0.819082	+	0.929505i
$406$	1.98379	+	6.75616i	0.0984537	+	0.335303i
$407$	−0.303846	+	0.227457i	−0.0150611	+	0.0112746i
$408$	−3.07025	+	0.219589i	−0.152000	+	0.0108713i
$409$	11.0059	+	17.1255i	0.544206	+	0.846802i	0.999041	−	0.0437740i	$-0.0139382\pi$
$409$	11.0059	+	17.1255i	0.544206	+	0.846802i	−0.454835	+	0.890576i	$0.650302\pi$
$410$	2.80878	−	7.72668i	0.138716	−	0.381593i
$411$	11.9316	−	40.6352i	0.588541	−	2.00439i
$412$	0.297569	+	0.797815i	0.0146602	+	0.0393055i
$413$	−15.2520	−	15.2520i	−0.750503	−	0.750503i
$414$	−8.40705	−	2.27526i	−0.413184	−	0.111823i
$415$	17.7638	+	31.8971i	0.871992	+	1.56577i
$416$	1.11371	−	2.43868i	0.0546040	−	0.119566i
$417$	17.0545	+	31.2330i	0.835164	+	1.52949i
$418$	−6.51705	−	0.466109i	−0.318759	−	0.0227981i
$419$	0.743296	−	0.477687i	0.0363124	−	0.0233366i	−0.522359	−	0.852726i	$-0.674948\pi$
$419$	0.743296	−	0.477687i	0.0363124	−	0.0233366i	0.558671	+	0.829389i	$0.311311\pi$
$420$	6.19111	−	4.05208i	0.302095	−	0.197721i
$421$	2.70401	+	0.388778i	0.131785	+	0.0189479i	0.207892	−	0.978152i	$-0.433340\pi$
$421$	2.70401	+	0.388778i	0.131785	+	0.0189479i	−0.0761065	+	0.997100i	$0.524249\pi$
$422$	−15.2435	−	8.32359i	−0.742043	−	0.405186i
$423$	1.04755	−	0.227881i	0.0509337	−	0.0110800i
$424$	−1.61237	−	11.2143i	−0.0783036	−	0.544614i
$425$	4.29575	+	5.54340i	0.208374	+	0.268894i
$426$	8.93938	+	19.5745i	0.433114	+	0.948388i
$427$	8.70102	−	11.6232i	0.421072	−	0.562486i
$428$	2.07566	+	9.54164i	0.100331	+	0.461212i
$429$	8.67142	−	2.54616i	0.418660	−	0.122930i
$430$	−3.37497	−	1.50743i	−0.162756	−	0.0726949i
$431$	−12.7416	−	11.0407i	−0.613741	−	0.531810i	0.291575	−	0.956548i	$-0.405821\pi$
$431$	−12.7416	−	11.0407i	−0.613741	−	0.531810i	−0.905316	+	0.424738i	$0.860366\pi$
$432$	2.53885	+	0.552293i	0.122150	+	0.0265722i
$433$	0.177228	−	2.47797i	0.00851702	−	0.119084i	−0.991415	−	0.130754i	$-0.958260\pi$
$433$	0.177228	−	2.47797i	0.00851702	−	0.119084i	0.999932	+	0.0116702i	$0.00371483\pi$
$434$	−7.52553	−	2.20970i	−0.361237	−	0.106069i
$435$	−22.8428	+	1.82521i	−1.09523	+	0.0875122i
$436$		−	8.05663i		−	0.385843i
$437$	16.0663	−	12.5696i	0.768553	−	0.601286i
$438$	12.1715	−	12.1715i	0.581575	−	0.581575i
$439$	20.2997	+	9.27058i	0.968854	+	0.442461i	0.836033	−	0.548679i	$-0.184869\pi$
$439$	20.2997	+	9.27058i	0.968854	+	0.442461i	0.132821	+	0.991140i	$0.457596\pi$
$440$	−0.758061	−	3.35008i	−0.0361391	−	0.159709i
$441$	−5.62092	−	6.48689i	−0.267663	−	0.308900i
$442$	−0.799314	+	3.67439i	−0.0380195	+	0.174773i
$443$	2.80246	+	39.1835i	0.133149	+	1.86166i	0.424990	+	0.905198i	$0.360278\pi$
$443$	2.80246	+	39.1835i	0.133149	+	1.86166i	−0.291841	+	0.956467i	$0.594268\pi$
$444$	0.0771707	−	0.536734i	0.00366236	−	0.0254723i
$445$	34.1455	−	0.284574i	1.61865	−	0.0134901i
$446$	9.00640	+	5.78806i	0.426465	+	0.274073i
$447$	−18.0307	−	13.4976i	−0.852821	−	0.638414i
$448$	0.526939	−	1.41278i	0.0248955	−	0.0667475i
$449$	−18.9649	+	8.66100i	−0.895011	+	0.408738i	−0.809173	−	0.587571i	$-0.800084\pi$
$449$	−18.9649	+	8.66100i	−0.895011	+	0.408738i	−0.0858387	+	0.996309i	$0.527357\pi$
$450$	3.31459	+	8.45370i	0.156251	+	0.398511i
$451$	3.05339	−	4.75116i	0.143778	−	0.223723i
$452$	6.51968	−	11.9399i	0.306660	−	0.561606i
$453$	−14.7662	−	19.7253i	−0.693775	−	0.926775i
$454$	−8.13263	+	9.38555i	−0.381683	+	0.440486i
$455$	−2.61884	−	8.65156i	−0.122773	−	0.405591i
$456$	7.05454	−	6.11280i	0.330359	−	0.286258i
$457$	−32.0815	+	17.5178i	−1.50071	+	0.819450i	−0.998961	−	0.0455624i	$-0.985492\pi$
$457$	−32.0815	+	17.5178i	−1.50071	+	0.819450i	−0.501750	+	0.865013i	$0.667310\pi$
$458$	−14.9225	+	5.56581i	−0.697284	+	0.260073i
$459$	−3.64429			−0.170101
$460$	8.77145	+	6.16941i	0.408971	+	0.287650i
$461$	−31.0792			−1.44750			−0.723751	−	0.690062i	$-0.757583\pi$
$461$	−31.0792			−1.44750			−0.723751	+	0.690062i	$0.757583\pi$
$462$	4.76249	−	1.77632i	0.221571	−	0.0826417i
$463$	12.5272	−	6.84038i	0.582190	−	0.317900i	−0.161027	−	0.986950i	$-0.551481\pi$
$463$	12.5272	−	6.84038i	0.582190	−	0.317900i	0.743217	+	0.669050i	$0.233299\pi$
$464$	−3.52921	+	3.05808i	−0.163840	+	0.141968i
$465$	12.0458	−	22.5041i	0.558609	−	1.04360i
$466$	−3.43673	+	3.96619i	−0.159203	+	0.183730i
$467$	17.0524	+	22.7793i	0.789090	+	1.05410i	0.997110	+	0.0759765i	$0.0242074\pi$
$467$	17.0524	+	22.7793i	0.789090	+	1.05410i	−0.208019	+	0.978125i	$0.566702\pi$
$468$	−2.33335	+	4.27320i	−0.107859	+	0.197529i
$469$	−8.85090	+	13.7723i	−0.408697	+	0.635944i
$470$	−1.30808	−	0.176959i	−0.0603371	−	0.00816253i
$471$	4.12612	−	1.88433i	0.190121	−	0.0868255i
$472$	4.99905	−	13.4030i	0.230100	−	0.616922i
$473$	−2.03274	−	1.52169i	−0.0934656	−	0.0699675i
$474$	−6.04764	−	3.88658i	−0.277777	−	0.178517i
$475$	−20.5030	−	5.65079i	−0.940742	−	0.259276i
$476$	−0.300985	+	2.09340i	−0.0137956	+	0.0959506i
$477$	1.46782	+	20.5228i	0.0672067	+	0.939673i
$478$	−5.04820	+	23.2062i	−0.230899	+	1.06143i
$479$	19.2836	+	22.2545i	0.881092	+	1.01683i	0.999714	+	0.0238954i	$0.00760687\pi$
$479$	19.2836	+	22.2545i	0.881092	+	1.01683i	−0.118622	+	0.992939i	$0.537848\pi$
$480$	4.15014	+	2.61852i	0.189427	+	0.119518i
$481$	−0.602574	−	0.275187i	−0.0274750	−	0.0125474i
$482$	−8.19975	+	8.19975i	−0.373489	+	0.373489i
$483$	−7.30723	+	14.0872i	−0.332491	+	0.640992i
$484$			8.64046i			0.392748i
$485$	−2.73154	−	34.1857i	−0.124033	−	1.55229i
$486$	−15.9994	−	4.69784i	−0.725746	−	0.213098i
$487$	0.791595	−	11.0679i	0.0358706	−	0.501537i	−0.947480	−	0.319816i	$-0.896379\pi$
$487$	0.791595	−	11.0679i	0.0358706	−	0.501537i	0.983350	−	0.181720i	$-0.0581666\pi$
$488$	9.40901	+	2.04681i	0.425926	+	0.0926545i
$489$	0.0502370	+	0.0435306i	0.00227180	+	0.00196852i
$490$	3.77572	+	9.87106i	0.170570	+	0.445929i
$491$	−8.63758	+	2.53622i	−0.389808	+	0.114458i	−0.470763	−	0.882260i	$-0.656021\pi$
$491$	−8.63758	+	2.53622i	−0.389808	+	0.114458i	0.0809546	+	0.996718i	$0.474203\pi$
$492$	1.71513	+	7.88432i	0.0773240	+	0.355453i
$493$	3.92523	−	5.24349i	0.176783	−	0.236155i
$494$	−4.73714	−	10.3729i	−0.213134	−	0.466698i
$495$	0.939150	+	6.16665i	0.0422116	+	0.277170i
$496$	−0.740266	−	5.14866i	−0.0332389	−	0.231182i
$497$	14.4477	−	3.14289i	0.648066	−	0.140978i
$498$	−31.4491	−	17.1725i	−1.40927	−	0.769519i
$499$	−14.6930	−	2.11254i	−0.657751	−	0.0945703i	−0.194646	−	0.980874i	$-0.562356\pi$
$499$	−14.6930	−	2.11254i	−0.657751	−	0.0945703i	−0.463105	+	0.886303i	$0.653265\pi$
$500$	−0.279500	−	11.1768i	−0.0124996	−	0.499844i
$501$	3.73067	−	2.39756i	0.166674	−	0.107115i
$502$	−5.47508	−	0.391585i	−0.244365	−	0.0174773i
$503$	−1.63435	−	2.99310i	−0.0728723	−	0.133456i	0.838703	−	0.544590i	$-0.183315\pi$
$503$	−1.63435	−	2.99310i	−0.0728723	−	0.133456i	−0.911575	+	0.411134i	$0.865133\pi$
$504$	−1.13755	+	2.49088i	−0.0506704	+	0.110953i
$505$	−2.37804	−	0.676782i	−0.105822	−	0.0301164i
$506$	4.94166	+	5.46347i	0.219684	+	0.242881i
$507$	−9.01975	−	9.01975i	−0.400581	−	0.400581i
$508$	−4.73936	−	12.7067i	−0.210275	−	0.563770i
$509$	0.751220	−	2.55842i	0.0332973	−	0.113400i	−0.941168	−	0.337940i	$-0.890270\pi$
$509$	0.751220	−	2.55842i	0.0332973	−	0.113400i	0.974465	+	0.224540i	$0.0720880\pi$
$510$	−6.46869	−	2.35148i	−0.286438	−	0.104125i
$511$	−6.39410	−	9.94941i	−0.282858	−	0.440136i
$512$	0.997452	−	0.0713392i	0.0440816	−	0.00315278i
$513$	8.84720	−	6.62293i	0.390613	−	0.292409i
$514$	−0.192434	−	0.655369i	−0.00848789	−	0.0289071i
$515$	−0.119999	+	1.90023i	−0.00528778	+	0.0837342i
$516$	3.59077	−	0.516274i	0.158075	−	0.0227277i
$517$	−0.849605	−	0.316886i	−0.0373656	−	0.0139366i
$518$	−0.349085	−	0.130202i	−0.0153379	−	0.00572074i
$519$	−50.4777	+	7.25760i	−2.21572	+	0.318573i
$520$	4.49768	−	3.96337i	0.197236	−	0.173805i
$521$	−1.45605	−	4.95884i	−0.0637906	−	0.217251i	0.921429	−	0.388547i	$-0.127023\pi$
$521$	−1.45605	−	4.95884i	−0.0637906	−	0.217251i	−0.985220	+	0.171296i	$0.945205\pi$
$522$	6.78912	−	5.08227i	0.297152	−	0.222445i
$523$	−41.9022	+	2.99691i	−1.83226	+	0.131046i	−0.944342	−	0.328965i	$-0.893300\pi$
$523$	−41.9022	+	2.99691i	−1.83226	+	0.131046i	−0.887914	+	0.460010i	$0.847846\pi$
$524$	8.94841	+	13.9240i	0.390913	+	0.608272i
$525$	16.3353	−	2.62727i	0.712933	−	0.114663i
$526$	−1.99330	+	6.78854i	−0.0869118	+	0.295995i
$527$	2.54963	+	6.83581i	0.111063	+	0.297773i
$528$	2.38366	+	2.38366i	0.103736	+	0.103736i
$529$	−22.8846	−	2.30104i	−0.994983	−	0.100045i
$530$	6.93452	−	24.3662i	0.301216	−	1.05840i
$531$	−10.7919	+	23.6309i	−0.468327	+	1.02549i
$532$	−3.07372	−	5.62910i	−0.133263	−	0.244052i
$533$	9.83194	+	0.703194i	0.425869	+	0.0304587i
$534$	−28.1927	+	18.1183i	−1.22002	+	0.784058i
$535$	−4.46334	+	21.3737i	−0.192967	+	0.924065i
$536$	−10.7468	−	1.54515i	−0.464189	−	0.0667403i
$537$	−43.7979	−	23.9155i	−1.89002	−	1.03203i
$538$	22.4285	−	4.87902i	0.966960	−	0.210349i
$539$	1.03322	+	7.18622i	0.0445040	+	0.309532i
$540$	4.67985	+	3.44281i	0.201389	+	0.148155i
$541$	13.5020	+	29.5652i	0.580495	+	1.27111i	0.941018	+	0.338357i	$0.109871\pi$
$541$	13.5020	+	29.5652i	0.580495	+	1.27111i	−0.360523	+	0.932750i	$0.617402\pi$
$542$	3.15813	−	4.21877i	0.135653	−	0.181211i
$543$	4.10862	+	18.8870i	0.176318	+	0.810520i
$544$	−1.34579	+	0.395160i	−0.0577004	+	0.0169424i
$545$	7.34695	−	16.4490i	0.314709	−	0.704597i
$546$	6.70456	+	5.80953i	0.286929	+	0.248625i
$547$	6.45324	+	1.40382i	0.275921	+	0.0600229i	0.348396	−	0.937347i	$-0.386726\pi$
$547$	6.45324	+	1.40382i	0.275921	+	0.0600229i	−0.0724756	+	0.997370i	$0.523090\pi$
$548$	1.37671	−	19.2490i	0.0588102	−	0.822275i
$549$	−16.7786	−	4.92664i	−0.716092	−	0.210264i
$550$	1.50728	−	7.53105i	0.0642704	−	0.321125i
$551$			19.8630i			0.846193i
$552$	−10.5115	−	0.527134i	−0.447399	−	0.0224363i
$553$	−3.49266	+	3.49266i	−0.148523	+	0.148523i
$554$	−9.63660	−	4.40089i	−0.409420	−	0.186976i
$555$	0.647012	−	1.02546i	0.0274641	−	0.0435284i
$556$	10.6190	+	12.2549i	0.450344	+	0.519725i
$557$	−1.68408	+	7.74160i	−0.0713569	+	0.328022i	−0.998963	−	0.0455386i	$-0.985500\pi$
$557$	−1.68408	+	7.74160i	−0.0713569	+	0.328022i	0.927606	+	0.373561i	$0.121863\pi$
$558$	0.673899	+	9.42234i	0.0285284	+	0.398880i
$559$	0.630701	−	4.38662i	0.0266758	−	0.185534i
$560$	2.36417	−	2.40391i	0.0999043	−	0.101584i
$561$	−3.97762	−	2.55626i	−0.167935	−	0.107925i
$562$	−2.21627	−	1.65908i	−0.0934877	−	0.0699840i
$563$	7.50551	−	20.1230i	0.316319	−	0.848085i	−0.677342	−	0.735669i	$-0.736868\pi$
$563$	7.50551	−	20.1230i	0.316319	−	0.848085i	0.993661	−	0.112417i	$-0.0358591\pi$
$564$	1.17841	−	0.538164i	0.0496202	−	0.0226608i
$565$	24.1992	−	18.4320i	1.01807	−	0.775438i
$566$	−10.3901	+	16.1673i	−0.436727	+	0.679561i
$567$	−8.05746	+	14.7561i	−0.338382	+	0.619700i
$568$	5.87635	+	7.84988i	0.246566	+	0.329374i
$569$	22.9223	−	26.4538i	0.960954	−	1.10900i	−0.0330277	−	0.999454i	$-0.510515\pi$
$569$	22.9223	−	26.4538i	0.960954	−	1.10900i	0.993982	−	0.109546i	$-0.0349396\pi$
$570$	19.9774	−	6.04718i	0.836760	−	0.253289i
$571$	−19.1362	+	16.5816i	−0.800826	+	0.693920i	−0.955806	−	0.293998i	$-0.905014\pi$
$571$	−19.1362	+	16.5816i	−0.800826	+	0.693920i	0.154980	+	0.987918i	$0.450469\pi$
$572$	3.61442	−	1.97362i	0.151126	−	0.0825212i
$573$	25.9300	−	9.67140i	1.08324	−	0.404028i
$574$	5.54392			0.231399
$575$	12.2824	+	20.5947i	0.512214	+	0.858858i
$576$	−1.81606			−0.0756690
$577$	−12.0298	+	4.48689i	−0.500808	+	0.186792i	−0.587157	−	0.809473i	$-0.699753\pi$
$577$	−12.0298	+	4.48689i	−0.500808	+	0.186792i	0.0863486	+	0.996265i	$0.472480\pi$
$578$	−13.1939	+	7.20440i	−0.548793	+	0.299664i
$579$	−4.68456	+	4.05920i	−0.194684	+	0.168694i
$580$	−9.99420	+	3.02526i	−0.414986	+	0.125617i
$581$	−16.1226	+	18.6064i	−0.668876	+	0.771924i
$582$	20.1704	+	26.9445i	0.836091	+	1.11689i
$583$	8.34046	−	15.2744i	0.345426	−	0.632601i
$584$	4.24054	−	6.59841i	0.175475	−	0.273044i
$585$	−8.66071	+	6.59666i	−0.358076	+	0.272738i
$586$	15.8120	−	7.22111i	0.653189	−	0.298301i
$587$	12.3465	−	33.1022i	0.509595	−	1.36628i	−0.386450	−	0.922311i	$-0.626299\pi$
$587$	12.3465	−	33.1022i	0.509595	−	1.36628i	0.896044	−	0.443965i	$-0.146429\pi$
$588$	−8.30346	−	6.21589i	−0.342429	−	0.256339i
$589$	−18.6127	−	11.9617i	−0.766923	−	0.492872i
$590$	22.4287	−	22.8057i	0.923377	−	0.938897i
$591$	6.63038	−	46.1153i	0.272738	−	1.89693i
$592$	−0.0176272	−	0.246461i	−0.000724475	−	0.0101295i
$593$	1.84067	−	8.46141i	0.0755871	−	0.347468i	−0.923785	−	0.382913i	$-0.874921\pi$
$593$	1.84067	−	8.46141i	0.0755871	−	0.347468i	0.999372	+	0.0354443i	$0.0112846\pi$
$594$	2.61360	+	3.01626i	0.107237	+	0.123759i
$595$	−2.52351	+	3.99955i	−0.103454	+	0.163966i
$596$	−9.33572	−	4.26348i	−0.382406	−	0.174639i
$597$	−8.61015	+	8.61015i	−0.352390	+	0.352390i
$598$	−4.23568	+	12.1397i	−0.173210	+	0.496427i
$599$			19.0334i			0.777683i	0.921305	+	0.388842i	$0.127125\pi$
$599$			19.0334i			0.777683i	−0.921305	+	0.388842i	$0.872875\pi$
$600$	6.08535	+	9.13071i	0.248433	+	0.372760i
$601$	38.3790	+	11.2691i	1.56551	+	0.459676i	0.945691	−	0.325066i	$-0.105386\pi$
$601$	38.3790	+	11.2691i	1.56551	+	0.459676i	0.619822	+	0.784742i	$0.287205\pi$
$602$	0.177816	−	2.48619i	0.00724724	−	0.101330i
$603$	19.2668	+	4.19124i	0.784605	+	0.170680i
$604$	−8.48539	−	7.35263i	−0.345266	−	0.299174i
$605$	−7.87934	+	17.6410i	−0.320341	+	0.717207i
$606$	2.32828	−	0.683643i	0.0945797	−	0.0277711i
$607$	2.68420	+	12.3391i	0.108948	+	0.500827i	0.998989	+	0.0449468i	$0.0143118\pi$
$607$	2.68420	+	12.3391i	0.108948	+	0.500827i	−0.890041	+	0.455880i	$0.849325\pi$
$608$	2.54902	−	3.40509i	0.103376	−	0.138095i
$609$	−6.41928	−	14.0563i	−0.260122	−	0.569588i
$610$	17.3436	+	12.7591i	0.702221	+	0.516601i
$611$	−0.225230	−	1.56651i	−0.00911181	−	0.0633741i
$612$	2.48900	−	0.541450i	0.100612	−	0.0218868i
$613$	36.3885	+	19.8696i	1.46972	+	0.802526i	0.996903	−	0.0786358i	$-0.0250564\pi$
$613$	36.3885	+	19.8696i	1.46972	+	0.802526i	0.472814	+	0.881162i	$0.343238\pi$
$614$	21.8390	+	3.13998i	0.881351	+	0.126719i
$615$	−3.68809	+	17.6612i	−0.148718	+	0.712169i
$616$	1.94849	−	1.25222i	0.0785070	−	0.0504534i
$617$	−7.78260	−	0.556623i	−0.313316	−	0.0224088i	−0.0862040	−	0.996278i	$-0.527474\pi$
$617$	−7.78260	−	0.556623i	−0.313316	−	0.0224088i	−0.227112	+	0.973869i	$0.572928\pi$
$618$	−0.895556	−	1.64009i	−0.0360245	−	0.0659740i
$619$	−0.910487	+	1.99369i	−0.0365956	+	0.0801331i	−0.927047	−	0.374945i	$-0.877661\pi$
$619$	−0.910487	+	1.99369i	−0.0365956	+	0.0801331i	0.890451	+	0.455078i	$0.150389\pi$
$620$	3.18375	−	11.1869i	0.127863	−	0.449278i
$621$	−12.3688	−	1.51032i	−0.496342	−	0.0606072i
$622$	4.20334	+	4.20334i	0.168539	+	0.168539i
$623$	8.04683	+	21.5744i	0.322389	+	0.864359i
$624$	−1.65757	+	5.64516i	−0.0663558	+	0.225987i
$625$	9.62166	−	23.0743i	0.384867	−	0.922972i
$626$	−8.86370	−	13.7922i	−0.354265	−	0.551247i
$627$	14.3020	−	1.02290i	0.571167	−	0.0408507i
$628$	1.65468	−	1.23868i	0.0660289	−	0.0494286i
$629$	0.0976405	+	0.332533i	0.00389318	+	0.0132590i
$630$	−4.59396	+	4.04821i	−0.183028	+	0.161285i
$631$	9.15752	−	1.31665i	0.364555	−	0.0524151i	0.0423967	−	0.999101i	$-0.486501\pi$
$631$	9.15752	−	1.31665i	0.364555	−	0.0524151i	0.322159	+	0.946686i	$0.395592\pi$
$632$	−3.06923	−	1.14476i	−0.122087	−	0.0455362i
$633$	35.7118	+	13.3198i	1.41942	+	0.529415i
$634$	−6.15756	+	0.885323i	−0.244548	+	0.0351607i
$635$	1.91121	−	30.2648i	0.0758442	−	1.20102i
$636$	7.00483	+	23.8562i	0.277759	+	0.945962i
$637$	−10.1438	+	7.59357i	−0.401913	+	0.300868i
$638$	−7.15494	+	0.511732i	−0.283267	+	0.0202597i
$639$	−9.62759	−	14.9808i	−0.380862	−	0.592632i
$640$	2.10152	+	0.763938i	0.0830700	+	0.0301973i
$641$	5.13824	−	17.4992i	0.202948	−	0.691178i	−0.793621	−	0.608413i	$-0.791807\pi$
$641$	5.13824	−	17.4992i	0.202948	−	0.691178i	0.996569	−	0.0827653i	$-0.0263752\pi$
$642$	−7.48879	−	20.0782i	−0.295559	−	0.792424i
$643$	−19.0448	−	19.0448i	−0.751052	−	0.751052i	0.223623	−	0.974676i	$-0.428211\pi$
$643$	−19.0448	−	19.0448i	−0.751052	−	0.751052i	−0.974676	+	0.223623i	$0.928211\pi$
$644$	−1.88912	+	6.98028i	−0.0744419	+	0.275061i
$645$	7.80196	+	2.22040i	0.307202	+	0.0874283i
$646$	−2.47836	+	5.42684i	−0.0975096	+	0.213516i
$647$	−20.8755	−	38.2306i	−0.820701	−	1.50300i	−0.863746	−	0.503928i	$-0.831888\pi$
$647$	−20.8755	−	38.2306i	−0.820701	−	1.50300i	0.0430450	−	0.999073i	$-0.486294\pi$
$648$	−11.1217	−	0.795440i	−0.436902	−	0.0312478i
$649$	18.4853	−	11.8798i	0.725610	−	0.466321i
$650$	12.7970	−	3.99040i	0.501941	−	0.156516i
$651$	17.0372	+	2.44958i	0.667740	+	0.0960066i
$652$	0.0265849	+	0.0145165i	0.00104115	+	0.000568509i
$653$	−6.46472	+	1.40631i	−0.252984	+	0.0550333i	−0.337269	−	0.941408i	$-0.609503\pi$
$653$	−6.46472	+	1.40631i	−0.252984	+	0.0550333i	0.0842848	+	0.996442i	$0.473139\pi$
$654$	2.51622	+	17.5007i	0.0983922	+	0.684333i
$655$	5.57222	+	36.5884i	0.217725	+	1.42963i
$656$	1.52736	+	3.34445i	0.0596333	+	0.130579i
$657$	−8.53630	+	11.4032i	−0.333033	+	0.444880i
$658$	−0.189207	−	0.869770i	−0.00737605	−	0.0339072i
$659$	−21.4005	+	6.28375i	−0.833645	+	0.244780i	−0.670582	−	0.741836i	$-0.733955\pi$
$659$	−21.4005	+	6.28375i	−0.833645	+	0.244780i	−0.163063	+	0.986616i	$0.552137\pi$
$660$	2.69296	+	7.04034i	0.104823	+	0.274045i
$661$	−29.0074	−	25.1351i	−1.12826	−	0.977641i	−0.128357	−	0.991728i	$-0.540970\pi$
$661$	−29.0074	−	25.1351i	−1.12826	−	0.977641i	−0.999901	+	0.0140871i	$0.995516\pi$
$662$	−0.504547	−	0.109757i	−0.0196098	−	0.00426585i
$663$	0.588707	−	8.23119i	0.0228635	−	0.319673i
$664$	−15.6664	−	4.60006i	−0.607973	−	0.178517i
$665$	−1.14227	−	14.2957i	−0.0442955	−	0.554364i
$666$			0.448731i			0.0173880i
$667$	15.4954	−	16.1697i	0.599983	−	0.626094i
$668$	1.42889	−	1.42889i	0.0552855	−	0.0552855i
$669$	−21.3715	−	9.76006i	−0.826272	−	0.377346i
$670$	−20.5323	−	12.9548i	−0.793231	−	0.500487i
$671$	9.68606	+	11.1783i	0.373926	+	0.431534i
$672$	−0.703390	+	3.23343i	−0.0271339	+	0.124732i
$673$	0.311051	+	4.34906i	0.0119901	+	0.167644i	0.999919	+	0.0127352i	$0.00405383\pi$
$673$	0.311051	+	4.34906i	0.0119901	+	0.167644i	−0.987929	+	0.154909i	$0.950492\pi$
$674$	3.69520	−	25.7007i	0.142334	−	0.989952i
$675$	6.41516	+	11.2967i	0.246920	+	0.434810i
$676$	−4.88980	−	3.14248i	−0.188069	−	0.120865i
$677$	18.0059	+	13.4790i	0.692021	+	0.518040i	0.886420	−	0.462882i	$-0.153185\pi$
$677$	18.0059	+	13.4790i	0.692021	+	0.518040i	−0.194399	+	0.980923i	$0.562276\pi$
$678$	−10.4331	+	27.9722i	−0.400681	+	1.07427i
$679$	21.0361	−	9.60685i	0.807290	−	0.368677i
$680$	−3.10802	−	0.420459i	−0.119187	−	0.0161239i
$681$	14.7345	−	22.9274i	0.564629	−	0.878579i
$682$	3.82924	−	7.01273i	0.146629	−	0.268531i
$683$	10.9856	+	14.6751i	0.420353	+	0.561525i	0.959869	−	0.280450i	$-0.0904837\pi$
$683$	10.9856	+	14.6751i	0.420353	+	0.561525i	−0.539516	+	0.841975i	$0.681393\pi$
$684$	−5.05852	+	5.83784i	−0.193417	+	0.223215i
$685$	20.3642	−	38.0446i	0.778075	−	1.45361i
$686$	−13.3629	+	11.5790i	−0.510197	+	0.442089i
$687$	30.6766	−	16.7507i	1.17039	−	0.639079i
$688$	1.54882	−	0.577680i	0.0590482	−	0.0220238i
$689$	30.3741			1.15716
$690$	−20.9803	−	10.6618i	−0.798706	−	0.405888i
$691$	−21.1779			−0.805644			−0.402822	−	0.915278i	$-0.631971\pi$
$691$	−21.1779			−0.805644			−0.402822	+	0.915278i	$0.631971\pi$
$692$	−21.7727	+	8.12081i	−0.827675	+	0.308707i
$693$	−3.69179	+	2.01587i	−0.140240	+	0.0765766i
$694$	−11.5654	+	10.0215i	−0.439016	+	0.380410i
$695$	10.5050	+	34.7041i	0.398476	+	1.31640i
$696$	6.71112	−	7.74504i	0.254384	−	0.293575i
$697$	−3.09046	−	4.12837i	−0.117060	−	0.156373i
$698$	−9.78648	+	17.9226i	−0.370424	+	0.678381i
$699$	6.22660	−	9.68877i	0.235512	−	0.366463i
$700$	7.01900	−	2.75207i	0.265293	−	0.104018i
$701$	37.1827	−	16.9808i	1.40437	−	0.641355i	0.438111	−	0.898921i	$-0.355648\pi$
$701$	37.1827	−	16.9808i	1.40437	−	0.641355i	0.966261	+	0.257566i	$0.0829205\pi$
$702$	−2.43427	+	6.52652i	−0.0918755	+	0.246328i
$703$	−0.841367	−	0.629839i	−0.0317327	−	0.0237548i
$704$	1.29223	+	0.830468i	0.0487029	+	0.0312994i
$705$	2.89669	−	0.0241414i	0.109096	−	0.000909220i
$706$	3.22636	−	22.4399i	0.121426	−	0.844535i
$707$	−0.118941	−	1.66302i	−0.00447325	−	0.0625442i
$708$	−6.67303	+	30.6754i	−0.250788	+	1.15285i
$709$	30.1837	+	34.8338i	1.13357	+	1.30821i	0.945340	+	0.326086i	$0.105730\pi$
$709$	30.1837	+	34.8338i	1.13357	+	1.30821i	0.188231	+	0.982125i	$0.439725\pi$
$710$	4.83915	+	21.3856i	0.181610	+	0.802587i
$711$	5.41138	+	2.47129i	0.202943	+	0.0926808i
$712$	−10.7981	+	10.7981i	−0.404677	+	0.404677i
$713$	5.82047	+	24.2575i	0.217978	+	0.908451i
$714$		−	4.64131i		−	0.173697i
$715$	9.17922	−	0.733449i	0.343283	−	0.0274294i
$716$	−21.8179	−	6.40633i	−0.815375	−	0.239416i
$717$	3.71807	−	51.9855i	0.138854	−	1.94143i
$718$	1.86085	+	0.404804i	0.0694464	+	0.0151071i
$719$	−3.27101	−	2.83435i	−0.121988	−	0.105703i	0.591730	−	0.806136i	$-0.298445\pi$
$719$	−3.27101	−	2.83435i	−0.121988	−	0.105703i	−0.713719	+	0.700433i	$0.752990\pi$
$720$	−3.70779	−	1.65609i	−0.138181	−	0.0617186i
$721$	−1.23193	+	0.361727i	−0.0458794	+	0.0134714i
$722$	0.192976	+	0.887097i	0.00718182	+	0.0330143i
$723$	15.2507	−	20.3725i	0.567180	−	0.757663i
$724$	3.65881	+	8.01168i	0.135979	+	0.297752i
$725$	−23.1636	−	2.93726i	−0.860275	−	0.109087i
$726$	−2.69856	−	18.7689i	−0.100153	−	0.696580i
$727$	−31.4749	+	6.84695i	−1.16734	+	0.253939i	−0.754148	−	0.656705i	$-0.771950\pi$
$727$	−31.4749	+	6.84695i	−1.16734	+	0.253939i	−0.413192	+	0.910644i	$0.635586\pi$
$728$	3.54799	+	1.93735i	0.131497	+	0.0718029i
$729$	3.11141	+	0.447353i	0.115237	+	0.0165686i
$730$	14.6750	−	9.60477i	0.543144	−	0.355488i
$731$	−1.95051	+	1.25352i	−0.0721422	+	0.0463630i
$732$	−21.0776	−	1.50750i	−0.779052	−	0.0557189i
$733$	11.9748	+	21.9302i	0.442299	+	0.810010i	0.999797	−	0.0201685i	$-0.00642027\pi$
$733$	11.9748	+	21.9302i	0.442299	+	0.810010i	−0.557498	+	0.830178i	$0.688238\pi$
$734$	11.1764	−	24.4728i	0.412527	−	0.903308i
$735$	−11.2846	−	20.2628i	−0.416238	−	0.747406i
$736$	−4.73141	+	0.783436i	−0.174402	+	0.0288778i
$737$	−11.7929	−	11.7929i	−0.434396	−	0.434396i
$738$	−2.33341	−	6.25611i	−0.0858939	−	0.230291i
$739$	14.8514	−	50.5791i	0.546316	−	1.86058i	0.0382406	−	0.999269i	$-0.487825\pi$
$739$	14.8514	−	50.5791i	0.546316	−	1.86058i	0.508075	−	0.861313i	$-0.330357\pi$
$740$	0.188762	−	0.519267i	0.00693903	−	0.0190886i
$741$	13.5297	+	21.0526i	0.497026	+	0.773388i
$742$	17.0398	−	1.21871i	0.625551	−	0.0447403i
$743$	−28.0287	+	20.9820i	−1.02827	+	0.769756i	−0.973487	−	0.228742i	$-0.926539\pi$
$743$	−28.0287	+	20.9820i	−1.02827	+	0.769756i	−0.0547871	+	0.998498i	$0.517448\pi$
$744$	3.21603	+	10.9528i	0.117905	+	0.401549i
$745$	−15.1725	−	17.2180i	−0.555879	−	0.630818i
$746$	−13.0184	+	1.87176i	−0.476637	+	0.0685300i
$747$	27.7826	+	10.3624i	1.01651	+	0.379139i
$748$	−2.01868	−	0.752927i	−0.0738101	−	0.0275298i
$749$	−14.5740	+	2.09542i	−0.532521	+	0.0765650i
$750$	4.09786	+	24.1912i	0.149633	+	0.883338i
$751$	10.1121	+	34.4385i	0.368994	+	1.25668i	0.909629	+	0.415422i	$0.136366\pi$
$751$	10.1121	+	34.4385i	0.368994	+	1.25668i	−0.540634	+	0.841258i	$0.681816\pi$
$752$	0.472575	−	0.353765i	0.0172330	−	0.0129005i
$753$	12.0153	−	0.859354i	0.437863	−	0.0313166i
$754$	−6.76858	−	10.5321i	−0.246497	−	0.383557i
$755$	−10.6194	−	22.7496i	−0.386480	−	0.827942i
$756$	−1.10375	+	3.75904i	−0.0401431	+	0.136715i
$757$	1.20919	+	3.24195i	0.0439486	+	0.117831i	0.957070	−	0.289857i	$-0.0936078\pi$
$757$	1.20919	+	3.24195i	0.0439486	+	0.117831i	−0.913121	+	0.407688i	$0.866335\pi$
$758$	14.9148	+	14.9148i	0.541728	+	0.541728i
$759$	−12.4407	−	10.3244i	−0.451568	−	0.374754i
$760$	8.30940	−	4.62759i	0.301414	−	0.167860i
$761$	15.2032	−	33.2904i	0.551116	−	1.20678i	−0.405143	−	0.914253i	$-0.632778\pi$
$761$	15.2032	−	33.2904i	0.551116	−	1.20678i	0.956259	−	0.292522i	$-0.0944945\pi$
$762$	14.2634	+	26.1215i	0.516710	+	0.946284i
$763$	12.1172	+	0.866642i	0.438673	+	0.0313745i
$764$	10.6088	−	6.81788i	0.383814	−	0.246662i
$765$	5.57548	+	1.16429i	0.201582	+	0.0420951i
$766$	−10.4827	−	1.50718i	−0.378755	−	0.0544568i
$767$	33.6596	+	18.3795i	1.21538	+	0.663646i
$768$	−2.14440	+	0.466485i	−0.0773793	+	0.0168328i
$769$	4.93047	+	34.2922i	0.177797	+	1.23661i	0.861845	+	0.507171i	$0.169309\pi$
$769$	4.93047	+	34.2922i	0.177797	+	1.23661i	−0.684048	+	0.729437i	$0.739782\pi$
$770$	5.12010	−	0.779765i	0.184515	−	0.0281008i
$771$	0.622690	+	1.36350i	0.0224256	+	0.0491053i
$772$	−1.69267	+	2.26115i	−0.0609207	+	0.0813805i
$773$	−3.17436	−	14.5923i	−0.114174	−	0.524848i	−0.998336	−	0.0576679i	$-0.981634\pi$
$773$	−3.17436	−	14.5923i	−0.114174	−	0.524848i	0.884162	−	0.467180i	$-0.154730\pi$
$774$	−2.88042	+	0.845767i	−0.103535	+	0.0304005i
$775$	16.7017	−	19.9367i	0.599942	−	0.716147i
$776$	11.5909	+	10.0436i	0.416091	+	0.360545i
$777$	0.798951	+	0.173801i	0.0286622	+	0.00623508i
$778$	0.397627	−	5.55956i	0.0142556	−	0.199320i
$779$	15.0053	+	4.40596i	0.537622	+	0.157860i
$780$	−8.53210	+	10.0140i	−0.305498	+	0.358558i
$781$			15.0624i			0.538974i
$782$	6.25108	−	2.48439i	0.223538	−	0.0888417i
$783$	8.57950	−	8.57950i	0.306606	−	0.306606i
$784$	−4.29928	−	1.96341i	−0.153546	−	0.0701219i
$785$	4.50787	−	1.02005i	0.160893	−	0.0364070i
$786$	−23.7866	−	27.4512i	−0.848438	−	0.979150i
$787$	1.88625	−	8.67096i	0.0672377	−	0.309086i	−0.931230	−	0.364433i	$-0.881263\pi$
$787$	1.88625	−	8.67096i	0.0672377	−	0.309086i	0.998467	+	0.0553467i	$0.0176264\pi$
$788$	−1.51451	−	21.1756i	−0.0539520	−	0.754348i
$789$	2.20969	−	15.3687i	0.0786669	−	0.547141i
$790$	−5.22243	−	5.13610i	−0.185806	−	0.182734i
$791$	17.2564	+	11.0900i	0.613566	+	0.394315i
$792$	−2.23320	−	1.67175i	−0.0793532	−	0.0594031i
$793$	−9.02143	+	24.1874i	−0.320360	+	0.858919i
$794$	27.4181	−	12.5214i	0.973033	−	0.444369i
$795$	−7.45328	+	55.0944i	−0.264341	+	1.95400i
$796$	−2.99978	+	4.66774i	−0.106324	+	0.165444i
$797$	−14.4856	+	26.5283i	−0.513105	+	0.939682i	0.484777	+	0.874638i	$0.338901\pi$
$797$	−14.4856	+	26.5283i	−0.513105	+	0.939682i	−0.997882	+	0.0650440i	$0.979281\pi$
$798$	8.43484	+	11.2676i	0.298590	+	0.398870i
$799$	−0.542216	+	0.625750i	−0.0191822	+	0.0221375i
$800$	3.59397	+	3.47612i	0.127066	+	0.122899i
$801$	20.9590	−	18.1611i	0.740551	−	0.641691i
$802$	5.39522	−	2.94602i	0.190512	−	0.104027i
$803$	11.2887	−	4.21045i	0.398368	−	0.148584i
$804$	23.8268			0.840308
$805$	−10.2224	+	12.5287i	−0.360291	+	0.441579i
$806$	13.9452			0.491200
$807$	−47.1956	+	17.6031i	−1.66137	+	0.619657i
$808$	0.970471	−	0.529917i	0.0341410	−	0.0186424i
$809$	−31.5359	+	27.3260i	−1.10874	+	0.960730i	−0.999446	−	0.0332792i	$-0.989405\pi$
$809$	−31.5359	+	27.3260i	−1.10874	+	0.960730i	−0.109296	+	0.994009i	$0.534860\pi$
$810$	−21.9815	−	11.7660i	−0.772350	−	0.413417i
$811$	23.7793	−	27.4428i	0.835004	−	0.963646i	−0.164738	−	0.986337i	$-0.552678\pi$
$811$	23.7793	−	27.4428i	0.835004	−	0.963646i	0.999743	+	0.0226912i	$0.00722344\pi$
$812$	−4.21975	−	5.63692i	−0.148084	−	0.197817i
$813$	−5.54254	+	10.1504i	−0.194385	+	0.355990i
$814$	0.205201	−	0.319299i	0.00719229	−	0.0111914i
$815$	0.0410399	+	0.0538810i	0.00143757	+	0.00188737i
$816$	2.79994	−	1.27869i	0.0980173	−	0.0447630i
$817$	2.45715	−	6.58788i	0.0859649	−	0.230481i
$818$	−16.2967	−	12.1996i	−0.569801	−	0.426548i
$819$	−6.17594	−	3.96903i	−0.215805	−	0.138689i
$820$	0.0685156	+	8.22108i	0.00239267	+	0.287092i
$821$	−5.13151	+	35.6904i	−0.179091	+	1.24560i	0.679781	+	0.733415i	$0.262075\pi$
$821$	−5.13151	+	35.6904i	−0.179091	+	1.24560i	−0.858872	+	0.512190i	$0.828834\pi$
$822$	3.02127	+	42.2428i	0.105379	+	1.47339i
$823$	4.93173	−	22.6708i	0.171909	−	0.790254i	−0.807740	−	0.589539i	$-0.799310\pi$
$823$	4.93173	−	22.6708i	0.171909	−	0.790254i	0.979650	−	0.200716i	$-0.0643268\pi$
$824$	−0.557615	−	0.643522i	−0.0194254	−	0.0224182i
$825$	−0.922048	+	16.8298i	−0.0321016	+	0.585938i
$826$	19.6204	+	8.96035i	0.682682	+	0.311770i
$827$	−25.1917	+	25.1917i	−0.876001	+	0.876001i	−0.993118	−	0.117117i	$-0.962635\pi$
$827$	−25.1917	+	25.1917i	−0.876001	+	0.876001i	0.117117	+	0.993118i	$0.462635\pi$
$828$	8.67211	−	0.806156i	0.301377	−	0.0280159i
$829$		−	14.8262i		−	0.514935i	−0.966287	−	0.257468i	$-0.917112\pi$
$829$		−	14.8262i		−	0.514935i	0.966287	−	0.257468i	$-0.0828881\pi$
$830$	−27.7907	−	23.6782i	−0.964630	−	0.821882i
$831$	22.3072	+	6.54999i	0.773829	+	0.227217i
$832$	−0.191257	+	2.67412i	−0.00663063	+	0.0927084i
$833$	6.47777	+	1.40915i	0.224442	+	0.0488243i
$834$	−26.8941	−	23.3038i	−0.931265	−	0.806946i
$835$	4.22035	−	1.61430i	0.146051	−	0.0558651i
$836$	6.26904	−	1.84076i	0.216819	−	0.0636639i
$837$	2.87281	+	13.2061i	0.0992988	+	0.456469i
$838$	−0.529496	+	0.707324i	−0.0182911	+	0.0244341i
$839$	−4.47425	−	9.79723i	−0.154468	−	0.338238i	0.816538	−	0.577291i	$-0.195890\pi$
$839$	−4.47425	−	9.79723i	−0.154468	−	0.338238i	−0.971006	+	0.239053i	$0.923163\pi$
$840$	−4.38470	+	5.96017i	−0.151286	+	0.205645i
$841$	−1.02364	−	7.11956i	−0.0352979	−	0.245502i
$842$	−2.66938	+	0.580689i	−0.0919930	+	0.0200119i
$843$	5.33237	+	2.91169i	0.183657	+	0.100284i
$844$	17.1912	+	2.47172i	0.591746	+	0.0850802i
$845$	−7.11768	−	10.8750i	−0.244856	−	0.374111i
$846$	−0.901868	+	0.579595i	−0.0310069	+	0.0199269i
$847$	−12.9953	−	0.929443i	−0.446524	−	0.0319360i
$848$	5.42970	+	9.94375i	0.186457	+	0.341470i
$849$	17.5201	−	38.3638i	0.601290	−	1.31664i
$850$	−5.96212	−	3.69268i	−0.204499	−	0.126658i
$851$	0.193580	+	1.16909i	0.00663583	+	0.0400758i
$852$	−15.2163	−	15.2163i	−0.521303	−	0.521303i
$853$	−8.60800	−	23.0789i	−0.294732	−	0.790208i	−0.996935	−	0.0782310i	$-0.975073\pi$
$853$	−8.60800	−	23.0789i	−0.294732	−	0.790208i	0.702203	−	0.711977i	$-0.252200\pi$
$854$	−4.09053	+	13.9311i	−0.139975	+	0.476711i
$855$	−15.6514	+	7.30602i	−0.535268	+	0.249860i
$856$	−5.27925	−	8.21467i	−0.180441	−	0.280771i
$857$	8.07178	−	0.577305i	0.275727	−	0.0197204i	0.0672089	−	0.997739i	$-0.478591\pi$
$857$	8.07178	−	0.577305i	0.275727	−	0.0197204i	0.208518	+	0.978019i	$0.433136\pi$
$858$	−7.23489	+	5.41597i	−0.246995	+	0.184898i
$859$	11.9928	+	40.8439i	0.409190	+	1.39357i	0.864227	+	0.503102i	$0.167808\pi$
$859$	11.9928	+	40.8439i	0.409190	+	1.39357i	−0.455037	+	0.890473i	$0.650374\pi$
$860$	3.68897	+	0.232957i	0.125793	+	0.00794377i
$861$	−12.0426	+	1.73146i	−0.410410	+	0.0590080i
$862$	15.7966	+	5.89181i	0.538033	+	0.200676i
$863$	−30.4114	−	11.3429i	−1.03522	−	0.386116i	−0.226312	−	0.974055i	$-0.572667\pi$
$863$	−30.4114	−	11.3429i	−1.03522	−	0.386116i	−0.808905	+	0.587939i	$0.799939\pi$
$864$	−2.57178	+	0.369766i	−0.0874937	+	0.0125797i
$865$	−51.8582	−	3.27483i	−1.76323	−	0.111347i
$866$	0.699907	+	2.38367i	0.0237838	+	0.0810003i
$867$	26.4099	−	19.7702i	0.896926	−	0.671430i
$868$	7.82326	−	0.559530i	0.265539	−	0.0189917i
$869$	−2.72042	−	4.23306i	−0.0922839	−	0.143597i
$870$	20.7647	−	9.69286i	0.703989	−	0.328619i
$871$	8.20061	−	27.9287i	0.277867	−	0.946328i
$872$	2.81550	+	7.54866i	0.0953450	+	0.255630i
$873$	−19.6950	−	19.6950i	−0.666574	−	0.666574i
$874$	−10.6607	+	17.3917i	−0.360602	+	0.588282i
$875$	16.8401	+	0.781909i	0.569300	+	0.0264334i
$876$	−7.15056	+	15.6575i	−0.241595	+	0.529020i
$877$	−0.716865	−	1.31284i	−0.0242068	−	0.0443315i	0.865296	−	0.501262i	$-0.167131\pi$
$877$	−0.716865	−	1.31284i	−0.0242068	−	0.0443315i	−0.889502	+	0.456930i	$0.848949\pi$
$878$	−22.2596	−	1.59204i	−0.751224	−	0.0537286i
$879$	−32.0918	+	20.6242i	−1.08243	+	0.695636i
$880$	1.88100	+	2.87395i	0.0634085	+	0.0968807i
$881$	−28.2461	−	4.06118i	−0.951636	−	0.136825i	−0.351025	−	0.936366i	$-0.614167\pi$
$881$	−28.2461	−	4.06118i	−0.951636	−	0.136825i	−0.600611	+	0.799542i	$0.705076\pi$
$882$	7.53346	+	4.11358i	0.253665	+	0.138511i
$883$	−50.8967	+	11.0719i	−1.71281	+	0.372599i	−0.958760	−	0.284217i	$-0.908267\pi$
$883$	−50.8967	+	11.0719i	−1.71281	+	0.372599i	−0.754051	+	0.656816i	$0.771903\pi$
$884$	−0.535150	−	3.72205i	−0.0179990	−	0.125186i
$885$	−41.5974	+	56.5438i	−1.39828	+	1.90070i
$886$	−16.3190	−	35.7336i	−0.548247	−	1.20049i
$887$	−20.1577	+	26.9276i	−0.676830	+	0.904139i	−0.999096	−	0.0425101i	$-0.986465\pi$
$887$	−20.1577	+	26.9276i	−0.676830	+	0.904139i	0.322266	+	0.946649i	$0.395555\pi$
$888$	0.115264	+	0.529861i	0.00386801	+	0.0177810i
$889$	19.6208	−	5.76119i	0.658061	−	0.193224i
$890$	−31.8932	+	12.1993i	−1.06906	+	0.408921i
$891$	−12.9441	−	11.2161i	−0.433643	−	0.375754i
$892$	−10.4613	−	2.27571i	−0.350269	−	0.0761964i
$893$	0.179127	−	2.50452i	0.00599424	−	0.0838104i
$894$	21.6107	+	6.34549i	0.722771	+	0.212225i
$895$	−38.7030	−	32.9757i	−1.29370	−	1.10225i
$896$			1.50785i			0.0503737i
$897$	5.40938	−	27.6928i	0.180614	−	0.924636i
$898$	14.7425	−	14.7425i	0.491963	−	0.491963i
$899$	−22.0955	−	10.0907i	−0.736925	−	0.336543i
$900$	−6.05987	−	6.76236i	−0.201996	−	0.225412i
$901$	−10.4064	−	12.0096i	−0.346687	−	0.400098i
$902$	−1.20051	+	5.51865i	−0.0399725	+	0.183751i
$903$	0.390226	+	5.45608i	0.0129859	+	0.181567i
$904$	−1.93604	+	13.4655i	−0.0643919	+	0.447855i
$905$	0.164130	+	19.6937i	0.00545588	+	0.654642i
$906$	20.7284	+	13.3214i	0.688656	+	0.442572i
$907$	6.08130	+	4.55240i	0.201926	+	0.151160i	0.695456	−	0.718569i	$-0.255203\pi$
$907$	6.08130	+	4.55240i	0.201926	+	0.151160i	−0.493529	+	0.869729i	$0.664293\pi$
$908$	4.33995	−	11.6359i	0.144026	−	0.386149i
$909$	−1.82659	+	0.834177i	−0.0605843	+	0.0276679i
$910$	5.47713	+	7.19088i	0.181565	+	0.238375i
$911$	3.29346	−	5.12473i	0.109117	−	0.169790i	−0.782400	−	0.622776i	$-0.786005\pi$
$911$	3.29346	−	5.12473i	0.109117	−	0.169790i	0.891518	+	0.452986i	$0.149641\pi$
$912$	−4.47355	+	8.19269i	−0.148134	+	0.271287i
$913$	−15.0303	−	20.0782i	−0.497432	−	0.664491i
$914$	23.9369	−	27.6247i	0.791763	−	0.913744i
$915$	−41.6589	−	22.2988i	−1.37720	−	0.737175i
$916$	12.0366	−	10.4298i	0.397701	−	0.344609i
$917$	−21.9044	+	11.9607i	−0.723346	+	0.394977i
$918$	3.41452	−	1.27355i	0.112696	−	0.0420334i
$919$	22.3661			0.737790			0.368895	−	0.929471i	$-0.379736\pi$
$919$	22.3661			0.737790			0.368895	+	0.929471i	$0.379736\pi$
$920$	−10.3744	−	2.71512i	−0.342034	−	0.0895147i
$921$	−48.4197			−1.59548
$922$	29.1196	−	10.8611i	0.959004	−	0.357690i
$923$	−23.0730	+	12.5988i	−0.759456	+	0.414695i
$924$	−3.84145	+	3.32864i	−0.126375	+	0.109504i
$925$	0.858916	−	0.888037i	0.0282410	−	0.0291985i
$926$	−9.34691	+	10.7869i	−0.307159	+	0.354480i
$927$	0.926708	+	1.23794i	0.0304371	+	0.0406592i
$928$	2.23801	−	4.09860i	0.0734662	−	0.134543i
$929$	−20.6640	+	32.1538i	−0.677963	+	1.05493i	0.316372	+	0.948635i	$0.397535\pi$
$929$	−20.6640	+	32.1538i	−0.677963	+	1.05493i	−0.994335	+	0.106296i	$0.966101\pi$
$930$	−3.42192	+	25.2947i	−0.112209	+	0.829447i
$931$	−18.2869	+	8.35135i	−0.599329	+	0.273705i
$932$	1.83400	−	4.91714i	0.0600746	−	0.161066i
$933$	−10.4433	−	7.81779i	−0.341900	−	0.255943i
$934$	−23.9378	−	15.3839i	−0.783268	−	0.503376i
$935$	−3.43487	−	3.37809i	−0.112332	−	0.110475i
$936$	0.692896	−	4.81920i	0.0226480	−	0.157520i
$937$	0.231615	+	3.23840i	0.00756653	+	0.105794i	0.999832	−	0.0183418i	$-0.00583872\pi$
$937$	0.231615	+	3.23840i	0.00756653	+	0.105794i	−0.992265	+	0.124136i	$0.960384\pi$
$938$	3.47993	−	15.9970i	0.113624	−	0.522320i
$939$	23.5614	+	27.1913i	0.768897	+	0.887355i
$940$	1.28744	−	0.291324i	0.0419918	−	0.00950195i
$941$	−51.9960	−	23.7458i	−1.69502	−	0.774091i	−0.998394	−	0.0566588i	$-0.981955\pi$
$941$	−51.9960	−	23.7458i	−1.69502	−	0.774091i	−0.696629	−	0.717432i	$-0.745317\pi$
$942$	−3.20746	+	3.20746i	−0.104505	+	0.104505i
$943$	−8.77812	−	15.2926i	−0.285855	−	0.497994i
$944$			14.3049i			0.465585i
$945$	−5.68141	+	6.66819i	−0.184816	+	0.216916i
$946$	2.43635	+	0.715378i	0.0792127	+	0.0232589i
$947$	−1.69427	+	23.6890i	−0.0550564	+	0.769788i	0.892671	+	0.450708i	$0.148828\pi$
$947$	−1.69427	+	23.6890i	−0.0550564	+	0.769788i	−0.947728	+	0.319080i	$0.896626\pi$
$948$	7.02455	+	1.52810i	0.228147	+	0.0496303i
$949$	15.8920	+	13.7705i	0.515876	+	0.447009i
$950$	21.1850	−	1.87055i	0.687333	−	0.0606888i
$951$	13.0990	−	3.84622i	0.424765	−	0.124722i
$952$	−0.449559	−	2.06659i	−0.0145703	−	0.0669786i
$953$	−22.4432	+	29.9806i	−0.727005	+	0.971166i	0.272953	+	0.962027i	$0.412000\pi$
$953$	−22.4432	+	29.9806i	−0.727005	+	0.971166i	−0.999958	+	0.00913810i	$0.997091\pi$
$954$	−8.54724	−	18.7159i	−0.276727	−	0.605948i
$955$	27.8770	−	4.24553i	0.902080	−	0.137382i
$956$	−3.37982	−	23.5072i	−0.109311	−	0.760277i
$957$	15.3822	−	3.34620i	0.497237	−	0.108167i
$958$	−25.8450	−	14.1124i	−0.835013	−	0.455952i
$959$	28.8025	+	4.14117i	0.930081	+	0.133725i
$960$	−4.80355	−	1.00310i	−0.155034	−	0.0323748i
$961$	−3.31731	+	2.13190i	−0.107010	+	0.0687711i
$962$	0.660750	+	0.0472578i	0.0213034	+	0.00152365i
$963$	8.49872	+	15.5642i	0.273867	+	0.501551i
$964$	4.81724	−	10.5483i	0.155153	−	0.339737i
$965$	−5.51785	+	3.07295i	−0.177626	+	0.0989216i
$966$	1.92352	−	15.7527i	0.0618883	−	0.506834i
$967$	−12.5789	−	12.5789i	−0.404512	−	0.404512i	0.475308	−	0.879820i	$-0.342337\pi$
$967$	−12.5789	−	12.5789i	−0.404512	−	0.404512i	−0.879820	+	0.475308i	$0.842337\pi$
$968$	−3.01953	−	8.09567i	−0.0970514	−	0.260205i
$969$	3.68862	−	12.5623i	0.118496	−	0.403559i
$970$	14.5060	+	31.0757i	0.465759	+	0.997780i
$971$	16.7743	+	26.1013i	0.538313	+	0.837632i	0.998746	−	0.0500628i	$-0.0159421\pi$
$971$	16.7743	+	26.1013i	0.538313	+	0.837632i	−0.460433	+	0.887695i	$0.652306\pi$
$972$	16.6323	−	1.18957i	0.533482	−	0.0381554i
$973$	−19.5738	+	14.6527i	−0.627506	+	0.469745i
$974$	3.12617	+	10.6467i	0.100169	+	0.341144i
$975$	−26.5516	+	12.6647i	−0.850332	+	0.405596i
$976$	−9.53106	+	1.37036i	−0.305082	+	0.0438641i
$977$	42.8589	+	15.9855i	1.37118	+	0.511423i	0.923784	−	0.382914i	$-0.125079\pi$
$977$	42.8589	+	15.9855i	1.37118	+	0.511423i	0.447394	+	0.894337i	$0.352352\pi$
$978$	−0.0622819	−	0.0232300i	−0.00199156	−	0.000742812i
$979$	−23.2185	+	3.33832i	−0.742068	+	0.106693i
$980$	−6.98724	−	7.92921i	−0.223199	−	0.253289i
$981$	−4.12211	−	14.0386i	−0.131609	−	0.448219i
$982$	7.20666	−	5.39484i	0.229974	−	0.172156i
$983$	42.0467	−	3.00724i	1.34108	−	0.0959161i	0.617727	−	0.786392i	$-0.288054\pi$
$983$	42.0467	−	3.00724i	1.34108	−	0.0959161i	0.723355	+	0.690476i	$0.242599\pi$
$984$	−4.36228	−	6.78784i	−0.139064	−	0.216388i
$985$	16.2181	−	44.6146i	0.516753	−	1.42154i
$986$	−1.84533	+	6.28461i	−0.0587672	+	0.200143i
$987$	0.682642	+	1.83023i	0.0217287	+	0.0582570i
$988$	8.06341	+	8.06341i	0.256531	+	0.256531i
$989$	−7.13955	+	3.44609i	−0.227025	+	0.109579i
$990$	−3.03496	−	5.44964i	−0.0964574	−	0.173201i
$991$	−4.41001	+	9.65659i	−0.140089	+	0.306752i	−0.966653	−	0.256091i	$-0.917565\pi$
$991$	−4.41001	+	9.65659i	−0.140089	+	0.306752i	0.826564	+	0.562843i	$0.190292\pi$
$992$	2.49286	+	4.56534i	0.0791485	+	0.144950i
$993$	1.13026	+	0.0808380i	0.0358678	+	0.00256532i
$994$	−12.4384	+	7.99367i	−0.394522	+	0.253544i
$995$	−10.3811	+	6.79446i	−0.329104	+	0.215399i
$996$	35.4674	+	5.09944i	1.12383	+	0.161582i
$997$	18.1258	+	9.89745i	0.574050	+	0.313455i	0.739923	−	0.672692i	$-0.234862\pi$
$997$	18.1258	+	9.89745i	0.574050	+	0.313455i	−0.165872	+	0.986147i	$0.553044\pi$
$998$	14.5049	−	3.15535i	0.459144	−	0.0998807i
$999$	0.0913658	+	0.635463i	0.00289068	+	0.0201052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.17.5	✓	240
5.3	odd	4	inner	230.2.l.a.63.11	yes	240
23.19	odd	22	inner	230.2.l.a.157.11	yes	240
115.88	even	44	inner	230.2.l.a.203.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.5	✓	240	1.1	even	1	trivial
230.2.l.a.63.11	yes	240	5.3	odd	4	inner
230.2.l.a.157.11	yes	240	23.19	odd	22	inner
230.2.l.a.203.5	yes	240	115.88	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.936950 + 0.349464i) q^{2} +(1.92611 - 1.05174i) q^{3} +(0.755750 - 0.654861i) q^{4} +(2.14017 - 0.647831i) q^{5} +(-1.43713 + 1.65853i) q^{6} +(0.903621 + 1.20710i) q^{7} +(-0.479249 + 0.877679i) q^{8} +(0.981834 - 1.52776i) q^{9} +(-1.77883 + 1.35490i) q^{10} +(-1.39727 + 0.638111i) q^{11} +(0.766917 - 2.05618i) q^{12} +(-2.14621 - 1.60663i) q^{13} +(-1.26848 - 0.815205i) q^{14} +(3.44085 - 3.49869i) q^{15} +(0.142315 - 0.989821i) q^{16} +(0.100061 + 1.39903i) q^{17} +(-0.386031 + 1.77455i) q^{18} +(-2.78544 - 3.21457i) q^{19} +(1.19319 - 1.89111i) q^{20} +(3.01002 + 1.37463i) q^{21} +(1.08617 - 1.08617i) q^{22} +(-0.240201 + 4.78981i) q^{23} +2.19455i q^{24} +(4.16063 - 2.77293i) q^{25} +(2.57235 + 0.755311i) q^{26} +(-0.185355 + 2.59161i) q^{27} +(1.47339 + 0.320516i) q^{28} +(-3.52921 - 3.05808i) q^{29} +(-2.00124 + 4.48055i) q^{30} +(4.99090 - 1.46546i) q^{31} +(0.212565 + 0.977147i) q^{32} +(-2.02017 + 2.69863i) q^{33} +(-0.582665 - 1.27586i) q^{34} +(2.71589 + 1.99799i) q^{35} +(-0.258452 - 1.79757i) q^{36} +(0.241444 - 0.0525229i) q^{37} +(3.73320 + 2.03848i) q^{38} +(-5.82360 - 0.837307i) q^{39} +(-0.457085 + 2.18885i) q^{40} +(-3.09304 + 1.98778i) q^{41} +(-3.30062 - 0.236065i) q^{42} +(0.792220 + 1.45084i) q^{43} +(-0.638111 + 1.39727i) q^{44} +(1.11156 - 3.90573i) q^{45} +(-1.44881 - 4.57176i) q^{46} +(0.417418 + 0.417418i) q^{47} +(-0.766917 - 2.05618i) q^{48} +(1.33158 - 4.53494i) q^{49} +(-2.92926 + 4.05209i) q^{50} +(1.66414 + 2.58946i) q^{51} +(-2.67412 + 0.191257i) q^{52} +(-9.06981 + 6.78958i) q^{53} +(-0.732005 - 2.49298i) q^{54} +(-2.57700 + 2.27086i) q^{55} +(-1.49250 + 0.214589i) q^{56} +(-8.74595 - 3.26207i) q^{57} +(4.37539 + 1.63193i) q^{58} +(-14.1593 + 2.03580i) q^{59} +(0.309270 - 4.89741i) q^{60} +(-2.71282 - 9.23902i) q^{61} +(-4.16410 + 3.11721i) q^{62} +(2.73136 - 0.195351i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(-5.63408 - 2.04808i) q^{65} +(0.949723 - 3.23446i) q^{66} +(3.79423 + 10.1727i) q^{67} +(0.991794 + 0.991794i) q^{68} +(4.57497 + 9.47834i) q^{69} +(-3.24288 - 0.922911i) q^{70} +(4.07344 - 8.91960i) q^{71} +(0.870343 + 1.59391i) q^{72} +(-7.82356 - 0.559552i) q^{73} +(-0.207866 + 0.133587i) q^{74} +(5.09744 - 9.71687i) q^{75} +(-4.21019 - 0.605334i) q^{76} +(-2.03286 - 1.11003i) q^{77} +(5.74902 - 1.25062i) q^{78} +(0.466190 + 3.24242i) q^{79} +(-0.336660 - 2.21058i) q^{80} +(4.63192 + 10.1425i) q^{81} +(2.20337 - 2.94335i) q^{82} +(3.47072 + 15.9546i) q^{83} +(3.17501 - 0.932268i) q^{84} +(1.12049 + 2.92935i) q^{85} +(-1.24929 - 1.08251i) q^{86} +(-10.0140 - 2.17840i) q^{87} +(0.109583 - 1.53217i) q^{88} +(14.6523 + 4.30230i) q^{89} +(0.323442 + 4.04792i) q^{90} -4.04247i q^{91} +(2.95513 + 3.77720i) q^{92} +(8.07176 - 8.07176i) q^{93} +(-0.536973 - 0.245227i) q^{94} +(-8.04381 - 5.07522i) q^{95} +(1.43713 + 1.65853i) q^{96} +(3.26012 - 14.9865i) q^{97} +(0.337177 + 4.71435i) q^{98} +(-0.397003 + 2.76121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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